Content-Type: multipart/mixed; boundary="-------------0204100908105" This is a multi-part message in MIME format. ---------------0204100908105 Content-Type: text/plain; name="02-180.comments" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="02-180.comments" Slightly corrected version of an article appeared in J. Phys. France 7 (1997) 1003-1018 ---------------0204100908105 Content-Type: text/plain; name="02-180.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="02-180.keywords" quasicrystals, model sets, torus parametrization ---------------0204100908105 Content-Type: application/postscript; name="torus2.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="torus2.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: torus2.dvi %%Pages: 20 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: Courier %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips torus2 %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2002.04.09:1116 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: 8r.enc % @@psencodingfile@{ % author = "S. 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b(gr)g(aphic)24 b Fo(pattern)i Fk(T)50 b Fo(\(where)27 b(the)e(p)s(erio)s(ds)g(of)f Fk(T)51 b Fo(span)26 b(the)g(en)m(tire)f (space\))-24 3168 y(consists)34 b(of)e(a)g(single)g(translation)e (class.)44 b(It)33 b(can)f(th)m(us)i(b)s(e)f(written)f(as:)1192 3439 y(LI\()p Fk(T)25 b Fo(\))j(=)1575 3299 y Fh(\032)1649 3439 y Fk(T)48 b Fo(+)22 b Fg(x)1942 3355 y Fh(\014)1942 3414 y(\014)2003 3439 y Fg(x)28 b Fk(2)g Fo(FD)o(\(\000\))2466 3299 y Fh(\033)3631 3439 y Fo(\(1\))-24 3717 y(where)35 b(FD)o(\(\000\))d(is)h(a)g(fundamen)m(tal)f(domain)f(of)h(the)i (underlying)e(translation)f(lattice)h(\000.)45 b(This)33 b(w)m(a)m(y)-8 b(,)-24 3837 y(w)m(e)26 b(obtain)d(a)i(one-to-one)e (corresp)s(ondence)k(b)s(et)m(w)m(een)g(the)e(elemen)m(ts)f(of)g(the)h (LI-class)g(and)f(the)h(p)s(oin)m(ts)-24 3957 y(of)i(FD)o(\(\000\).)41 b(The)28 b(translation)d(v)m(ector)j Fg(x)e Fo(hereb)m(y)j(marks)d(the) i(origin)c(of)j(space)h(relativ)m(e)e(to)g(the)h(lattice)-24 4078 y(and,)33 b(for)f(standardization,)f(the)i(pattern)g(with)f(a)g (lattice)f(p)s(oin)m(t)h(coinciding)e(with)i(the)h(origin)d(shall)-24 4198 y(b)s(e)k(parametrized)e(b)m(y)j(zero.)46 b(As)34 b(FD)o(\(\000\))f(forms)g(an)g Fi(n)p Fo(-dimensional)e(torus)j Fn(T)2886 4162 y Fm(n)2969 4198 y Fo(after)f(iden)m(ti\014cation)-24 4319 y(of)f(opp)s(osite)h(facets,)g(this)f(is)g(called)g(the)h Fl(torus)i(p)-5 b(ar)g(ametrization)p Fo(.)123 4439 y(The)24 b(k)m(ey)h(in)e(generalizing)f(this)h(concept)h(to)g(LI-classes)g(of)f (quasip)s(erio)s(dic)f(patterns)i(is)f(that)h(these)-24 4559 y(patterns)30 b(can)f(b)s(e)g(describ)s(ed)h(as)f(sections)g (through)g(p)s(erio)s(dic)e(structures)j(of)f(higher)f(dimension.)41 b(So)-24 4680 y(b)m(y)47 b(rev)m(ersing)f(the)g(cut-and-pro)5 b(ject)46 b(mec)m(hanism,)i(the)e(LI-class)f(can)h(b)s(e)f (parametrized)g(b)m(y)h(the)-24 4800 y(p)s(oin)m(ts)33 b(of)f(a)g(fundamen)m(tal)g(domain)e(of)j(the)g(em)m(b)s(edding)f (lattice:)123 4921 y(Let)c(\003)f Fk(\032)h Fn(R)559 4884 y Fm(n)640 4921 y Fo(b)s(e)g(the)g(em)m(b)s(edding)f(lattice)f (and)i Fi(E)34 b Fo(and)27 b Fi(E)2259 4936 y Fm(int)2384 4921 y Fo(the)h(ph)m(ysical)f(resp.)i(in)m(ternal)e(space,)-24 5041 y Fi(E)f Fo(+)19 b Fi(E)241 5056 y Fm(int)368 5041 y Fo(spanning)31 b Fn(R)845 5005 y Fm(n)898 5041 y Fo(.)43 b(Then)33 b(a)d(quasip)s(erio)s(dic)g(pattern)h Fk(T)54 b(\032)28 b Fi(E)37 b Fo(is)30 b(obtained)h(b)m(y)h(pro)5 b(jecting)31 b(all)-24 5161 y(those)j(lattice)d(p)s(oin)m(ts)h(in)m(to) g Fi(E)39 b Fo(\(parallel)30 b(to)i Fi(E)1708 5176 y Fm(int)1805 5161 y Fo(\))g(whic)m(h)h(pro)5 b(ject,)34 b(parallel)c(to)i Fi(E)6 b Fo(,)33 b(in)m(to)f(a)g(compact)1842 5471 y(2)p eop %%Page: 3 3 3 2 bop -24 407 a Fo(subset)46 b Fi(W)58 b Fo(of)44 b Fi(E)632 422 y Fm(int)729 407 y Fo(,)j(called)c(the)i(pro)5 b(jection)44 b(windo)m(w.)80 b(\(This)44 b(can)h(easily)e(b)s(e)i (extended)h(to)e(the)-24 527 y(situation)21 b(with)h(sev)m(eral)h (translation)d(classes)j(of)f(p)s(oin)m(ts)f(and)i(hence)g(a)f(system)h (of)f(windo)m(ws,)j(compare)-24 648 y([5]\).)42 b(F)-8 b(or)28 b(simplicit)m(y)-8 b(,)26 b(w)m(e)j(shall)e(also)g(assume)i (that)f Fi(W)42 b Fo(is)27 b(the)i(closure)f(of)g(its)f(in)m(terior)g (and)h(that)g Fi(@)5 b(W)-24 768 y Fo(is)27 b(of)g(zero)g(Leb)s(esgue)i (measure.)42 b(T)-8 b(ranslating)26 b(the)h(windo)m(w)h(b)m(y)g(a)f(v)m (ector)h Fg(t)h Fk(2)f Fi(E)2962 783 y Fm(int)3085 768 y Fo(t)m(ypically)e(results)-24 888 y(in)36 b(new,)j(but)e(lo)s(cally)e (isomorphic)f(patterns)k([5].)56 b(No)m(w)38 b(let)e Fg(t)h Fo(b)s(e)g(giv)m(en)g(as)g(the)g(pro)5 b(jection)37 b(image)-24 1009 y(of)i(some)g(p)s(oin)m(t)f Fg(x)g Fk(2)h Fo(FD\(\003\))f(while)g(the)i(pro)5 b(jection)39 b(of)f Fg(x)h Fo(on)g Fi(E)45 b Fo(shall)37 b(de\014ne)k(the)e(origin)e(of)h (the)-24 1129 y(ph)m(ysical)33 b(space.)44 b(This)33 b(w)m(a)m(y)-8 b(,)34 b(a)e(function)g Fi(f)38 b Fo(:)28 b(FD)o(\(\003\))g Fk(!)k Fo(LI[)p Fk(T)25 b Fo(])33 b(is)f(de\014ned.) 45 b(W)-8 b(e)33 b(no)m(w)g(assume)g(that)-24 1249 y(the)d(dimension)d (of)i(the)g(em)m(b)s(edding)f(lattice)g(\003)g(is)h(minimal)24 b(\(\003)29 b(pro)5 b(jects)30 b(densely)g(in)m(to)e Fi(E)3330 1264 y Fm(int)3427 1249 y Fo(\).)42 b(Then)-24 1370 y(the)25 b(function)g Fi(f)35 b Fo(is)24 b Fl(inje)-5 b(ctive)24 b Fo(since)h(w)m(e)h(restricted)f(its)f(domain)f(to)h(FD)o (\(\003\).)41 b(On)24 b(the)i(other)e(hand,)j Fi(f)35 b Fo(is)-24 1490 y(also)c Fl(surje)-5 b(ctive)32 b Fo({)f(with)h(one)g (subtlet)m(y)h(as)f(exception:)43 b(Whenev)m(er)35 b(the)d(pro)5 b(jection)31 b(of)h(some)f(lattice)-24 1611 y(p)s(oin)m(t)f(in)m(to)h Fi(E)498 1626 y Fm(int)625 1611 y Fo(coincides)g(with)f(a)h(b)s (oundary)g(p)s(oin)m(t)f(of)h(the)g(windo)m(w,)h(w)m(e)g(ha)m(v)m(e)g (to)f(mak)m(e)g(a)f(c)m(hoice)-24 1731 y(whether)39 b(to)d(include)h (this)g(p)s(oin)m(t)f(in)g(the)i(pattern)f(or)g(not,)h(corresp)s (onding)f(to)f(limiting)d(pro)s(cesses)-24 1851 y(of)41 b(windo)m(w)h(shifts)g(from)e(di\013eren)m(t)i(sides.)70 b(Eac)m(h)43 b(suc)m(h)g(limiting)37 b(pro)s(cess)42 b(results)g(in)f(a)g(so-called)-24 1972 y Fl(singular)29 b Fo(pro)5 b(jection)29 b(pattern)g(\(all)e(other)i(patterns)h(are)f (called)f(regular\).)41 b(Since)30 b(singular)d(patterns)-24 2092 y(also)42 b(b)s(elong)g(to)g(the)h(LI-class,)i(sev)m(eral)e (elemen)m(ts)g(here)g(corresp)s(ond)h(to)e(a)g(common)f(parameter.)-24 2213 y(Put)29 b(in)e(other)h(w)m(ords,)j(this)c(means)h(that)g(m)m (utually)f(singular)f(patterns)j(are)f(iden)m(ti\014ed)g(b)m(y)h(the)g (torus)-24 2333 y(parametrization.)40 b(As)29 b(a)f(matter)f(of)h (fact,)h(has)g Fi(@)5 b(W)42 b Fo(Leb)s(esgue)30 b(measure)f(zero,)g (almost)e(all)f(patterns)-24 2453 y(of)41 b(the)h(LI-class)f(are)g (regular)f(and)h(m)m(utually)f(singular)f(patterns)j(di\013er)f(only)f (in)h(mismatc)m(hes)f(of)-24 2574 y(zero)32 b(densit)m(y)h([5].)43 b(Tw)m(o)33 b(regular)d(patterns,)j(on)f(the)g(other)g(hand,)g(are)g (either)f(iden)m(tical)f(or)i(di\013er)f(in)-24 2694 y(mismatc)m(hes)e(of)g(p)s(ositiv)m(e)g(densit)m(y)-8 b(.)44 b(So)29 b(using)g(the)h(torus)g(parametrization)d(just)j(means)f (to)g(iden)m(tify)-24 2814 y(patterns)34 b(that)e(are)h(iden)m(tical)e Fl(almost)j(everywher)-5 b(e)32 b Fo(whic)m(h)h(is)f(also)g(reasonable) g(ph)m(ysically)-8 b(.)-24 3072 y Ff(Symmetry)37 b(analysis)-24 3256 y Fo(Considering)j(the)h(p)s(erio)s(dic)e(case,)k(the)e(torus)f (parametrization)e(can)i(b)s(e)h(used)g(to)f(determine)g(the)-24 3377 y(Wyc)m(k)m(o\013)i(p)s(ositions:)56 b(Giv)m(en)40 b(an)f(elemen)m(t)h Fi(g)j Fo(of)c(the)h(holohedry)-8 b(,)41 b(represen)m(ted)h(as)e(a)g(lattice)e(auto-)-24 3497 y(morphism)e(^)-53 b Fi(g)s Fo(,)34 b(the)g(corresp)s(onding)f (Wyc)m(k)m(o\013)j(p)s(osition)31 b(app)s(ears)j(as)g(the)g(set)g(of)f (all)f(\014xed)i(p)s(oin)m(ts)f(of)-20 3618 y(^)-53 b Fi(g)36 b Fo(on)d(the)g(torus)g Fn(T)p Fo(:)933 3738 y Fi(g)t Fo(\()p Fk(T)25 b Fo(\()p Fg(x)p Fo(\)\))i(=)h Fk(T)d Fo(\()p Fg(x)p Fo(\))111 b Fk(\()-17 b(\))113 b Fo(^)-52 b Fi(g)s Fo(\()p Fg(x)p Fo(\))27 b(=)h Fg(x)f Fo(\(mo)s(d)16 b 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Fn(T)k Fo(\(see)d([3])g(for)f(details)f(on)i(the)g(structure)g(of)g (subtori\).)123 4793 y(Ho)m(w)e(do)s(es)g(this)f(generalize)g(to)g(the) h(determination)e(of)h(symmetric)g(elemen)m(ts)g(of)g(quasip)s(erio)s (dic)-24 4913 y(LI-classes?)44 b(It)33 b(turns)g(out)g(that)f(there)h (are)g(t)m(w)m(o)g(conditions)f(in)g(this)g(case)h([3]:)96 5102 y(1.)48 b(The)32 b(corresp)s(onding)f(torus)g(parameter)f(m)m(ust) h(b)s(e)g(in)f(a)g Fl(Wycko\013)j(p)-5 b(osition)30 b Fo(of)g(the)i(symmetry)220 5222 y(considered)i(as)e(a)h(symmetry)g Fl(of)h(the)h(emb)-5 b(e)g(dding)33 b(lattic)-5 b(e)33 b Fo(\003.)1842 5471 y(3)p eop %%Page: 4 4 4 3 bop 96 407 a Fo(2.)48 b(The)34 b(symmetry)f(m)m(ust)f(b)s(elong)g (to)g(the)h(generalized)f(symmetry)h(group)f(of)g(the)h(LI-class.)-24 577 y(While)e(1.)g(trivially)e(implies)g(2.)j(for)f(crystallographic)f (LI-classes)i(\(eac)m(h)g(lattice)f(coincides)g(with)g(its)-24 698 y(em)m(b)s(edding)43 b(lattice)e(of)i(minimal)c(dimension\),)44 b(the)f(symmetry)h(m)m(ust)f(b)s(e)g(compatible)e(with)h(the)-24 818 y(pro)5 b(jection)46 b(pro)s(cedure)g(in)f(the)h(quasip)s(erio)s (dic)e(case:)71 b(The)46 b(generalized)f(symmetry)h(is)f(just)h(the)-24 939 y(maximal)40 b(subgroup)j(of)f(the)h(holohedry)g(of)f(\003)h(that)f (stabilizes)g Fi(E)48 b Fo(and)43 b Fi(E)2854 954 y Fm(int)2993 939 y Fo(together)g(with)f(the)-24 1059 y(pro)5 b(jection)33 b(windo)m(w.)123 1179 y(A)m(t)g(this)f(p)s(oin)m(t,)g(let)g(us)i (compare)e(our)h(approac)m(h)g(with)f(the)i(di\013eren)m(t)e(notion)g (of)g(sp)s(ecial)g(p)s(oin)m(ts)-24 1300 y(for)42 b(quasilattices)f (giv)m(en)h(in)g([4)o(].)72 b(While)41 b(b)s(oth)h(approac)m(hes)i(use) f(the)f(Wyc)m(k)m(o\013)i(p)s(ositions)d(of)g(the)-24 1420 y(higher)f(dimensional)d(em)m(b)s(edding)j(lattice)e(as)i(a)g (starting)e(p)s(oin)m(t,)j(in)e([4])h(sp)s(ecial)f(p)s(oin)m(ts)h(of)f (single)-24 1540 y(quasip)s(erio)s(dic)33 b(LI-class)h(mem)m(b)s(ers)g (are)g(de\014ned)h(b)m(y)g(pro)5 b(jecting)34 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(hains)h(with)-24 973 y Fi(I)27 937 y Fm(n)107 973 y Fo(as)e(exact)i(symmetry)f(and)1147 947 y(~)1129 973 y Fi(d)1180 988 y Fm(n)1260 973 y Fo(orbits)e(of)i(\()p Fk(\000)p Fi(I)1814 937 y Fm(n)1861 973 y Fo(\)-symmetric)e(c)m(hains.) -24 1371 y(consist)40 b(of)g(all)d(patterns)k(that)e(are)h(equiv)-5 b(alen)m(t)39 b(with)h(resp)s(ect)h(to)e(s)p 2513 1387 39 4 v 1 w(ymmetry)g(preserving)h(m)p 3452 1387 82 4 v(utual)-24 1492 y(l)p -24 1508 28 4 v -1 w(o)s(cal)32 b(d)p 207 1508 55 4 v(eriv)-5 b(abilit)m(y)30 b([2,)i(8]\).)44 b(But)32 b(there)i(is)e(more)g(to)g(b)s(e)h(said.)123 1612 y(F)-8 b(or)27 b(closer)h(insp)s(ection,)h(let)e(us)i(imp)s(ose)e (t)m(w)m(o)i(conditions)e(on)h(the)h(pro)5 b(jection)28 b(windo)m(w.)42 b(In)29 b(order)-24 1733 y(not)45 b(to)f(bring)g(along) f(an)m(y)i(restriction)f(to)g(the)h(geometrical)d(symmetries)j(w)m(e)g (shall)e(assume)i(the)-24 1853 y(windo)m(w)30 b(to)f(b)s(e)g(in)m(v)-5 b(arian)m(t)28 b(under)i(the)f(maximal)d(p)s(oin)m(t)j(group)f(that)h 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b(con)m(tains)e(the)h(L)-8 b(TM)33 b(of)f(the)h(sp)s(ecial)f (giv)m(en)h(LI-class.)123 4983 y(It)j(is)f(th)m(us)i(natural)e(to)g (reform)m(ulate)g(the)h(symmetry)h(analysis)e(without)g(explicit)g (reference)i(to)-24 5103 y(the)c(cut-and-pro)5 b(ject)33 b(formalism)c(and)j(without)g(\014xing)g(a)h(sp)s(eci\014c)g(represen)m (tation)g(in)e(form)h(of)f(the)1842 5471 y(8)p eop %%Page: 9 9 9 8 bop -24 407 a Fo(em)m(b)s(edding)33 b(lattice.)42 b(Let)32 b(us)i(explain)d(this)h(in)g(more)g(detail)f(for)h(L)-8 b(TM's)34 b(of)e(dimension)f(t)m(w)m(o.)-24 667 y Ff(Symmetry)37 b(analysis)g(from)g(a)h(n)m(um)m(b)s(er)f(theoretic)f(p)s(oin)m(t)h(of) g(view)-24 851 y Fo(Giv)m(en)44 b(a)f(sp)s(ecial)g(cut-and-pro)5 b(ject)44 b(tiling)d(class)i(in)g(2D,)g(the)h(total)e(n)m(um)m(b)s(ers) j(of)e(its)g(symmetric)-24 972 y(mem)m(b)s(ers)e(are)f(p)s(erhaps)h (most)f(easily)g(determined)g(b)m(y)h(calculating)d(determinan)m(ts)i (according)g(to)-24 1092 y(\(3\).)69 b(The)42 b(adv)-5 b(an)m(tage)41 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Fk(\002)31 b Fi(I)52 b Fo(generalized)44 b(symmetry)-8 b(.)80 b(If)-24 1681 y(m)m(ultiple)25 b(en)m(tries)j(in)f(the)h(same)f (column)f(o)s(ccur,)j(the)f(second)g(refers)h(to)e(orbits)f(of)h (mirror)f(symmetric)-24 1802 y(tilings)31 b(and)h(the)h(third)f(\(if)f (presen)m(t\))k(to)d(orbits)g(of)g(tilings)e(with)i(\()p Fi(I)2487 1766 y Fm(n=)p Fe(2)2627 1802 y Fk(\001)22 b Fi(S)6 b Fo(\)-symmetry)-8 b(.)-24 2200 y(and)47 b Fi(\030)228 2164 y Fe(5)298 2200 y Fk(\000)32 b Fo(1)51 b(=)g Fi(\034)687 2164 y Fj(\000)p Fe(1)782 2200 y Fo(\()p Fi(\034)873 2164 y Fe(3)944 2200 y Fk(\000)32 b Fo(1\).)84 b(On)47 b(restriction)e(to)h(mirror)e(symmetric)i(tilings)e(w)m(e)j (get)f(to)g(the)-24 2321 y(symmetry)37 b(structure)g(of)f (one-dimensional)e(Fib)s(onacci)g(c)m(hains)j(\(there)g(is)e(one)i (subtorus)g(for)f(eac)m(h)-24 2441 y(re\015ection)d(axes)h(in)e(this)g (case\).)44 b(In)33 b(summary)-8 b(,)32 b(w)m(e)i(\014nd:)122 2669 y Fk(\017)48 b Fo(There)36 b(is)f(one)g(tiling)d(with)j(full)e (symmetry)-8 b(,)35 b Fi(D)1999 2684 y Fe(10)2098 2669 y Fk(\002)24 b Fi(I)8 b Fo(.)50 b(It)35 b(is)g(singular)e(b)s(oth)i(in) f(the)h(P)m(enrose)220 2790 y(and)e(in)f(the)h(triangle)d(LI-class.)122 2993 y Fk(\017)48 b Fo(There)30 b(is)e(one)h(orbit)e(con)m(taining)h(4) g(tilings)e(with)i(\()p Fi(D)2175 3008 y Fe(5)2229 2993 y Fk(\002)14 b Fo(\()p Fi(C)2428 3008 y Fe(2)2481 2993 y Fk(\001)g Fi(I)2574 2957 y Fe(2)2613 2993 y Fo(\)\))28 b(-symmetry)-8 b(.)42 b(The)30 b(triangle)220 3114 y(tilings)g(are)j (singular,)e(but)i(the)g(patterns)g(of)f(the)h(P)m(enrose)i(LI-class)d (are)h(regular.)122 3317 y Fk(\017)48 b Fo(Finally)-8 b(,)40 b(there)h(is)f(an)h(orbit)e(of)h(15)g(tilings)f(with)h(\()p Fi(D)2242 3332 y Fe(2)2309 3317 y Fk(\002)28 b Fi(I)2465 3281 y Fe(3)2504 3317 y Fo(\)-symmetry)-8 b(,)42 b(singular)d(in)h(b)s (oth)220 3437 y(cases.)122 3641 y Fk(\017)48 b Fo(The)34 b(orbit)d(coun)m(ts)j(for)e(tilings)e(without)i(rotational)e(symmetry)j (are)f(sho)m(wn)i(in)e(T)-8 b(ab.)33 b(6.)-24 4009 y Ff(12-fold)38 b(rotational)e(symmetric)f(tilings)-24 4193 y Fo(The)30 b(underlying)d(mo)s(dule)g(b)s(elonging)f(to)i(t)m(w)m (elv)m(efold)h(symmetric)e(tilings,)g(lik)m(e)g(the)i(square-triangle) -24 4314 y(tiling,)40 b(the)h(Stamp\015i)f(tiling)e(or)i(the)h(So)s (colar)e(tiling,)h(is)h(the)g(mo)s(dule)e Fn(Z)p Fo([)p Fi(\030)5 b Fo(])38 b(with)i Fi(\030)46 b Fo(=)41 b Fi(e)3388 4250 y Fd(2)p Fc(\031)r(i)p 3388 4262 91 3 v 3403 4303 a Fd(12)3493 4314 y Fo(.)68 b(The)-24 4434 y(corresp)s(onding)43 b(cyclotomic)e(\014eld)h(is)g(the)h(splitting)d(\014eld)i(of)g(the)h (12th)f(cyclotomic)f(p)s(olynomial,)-24 4554 y Fi(P)39 4569 y Fe(12)114 4554 y Fo(\()p Fi(x)p Fo(\))29 b(=)g Fi(x)434 4518 y Fe(4)496 4554 y Fk(\000)23 b Fi(x)651 4518 y Fe(2)713 4554 y Fo(+)g(1)33 b([13)o(,)h(11)o(].)46 b(The)34 b(primitiv)m(e)d(12th)h(ro)s(ots)h(of)g(unit)m(y)g(are)g Fi(\030)5 b(;)17 b(\030)3035 4518 y Fe(5)3073 4554 y Fi(;)g(\030)3165 4518 y Fe(7)3204 4554 y Fi(;)g(\030)3296 4518 y Fe(11)3370 4554 y Fo(,)33 b(and)g(the)-24 4675 y(Galois)e(group)h(is)g Fk(G)i(')28 b Fi(C)918 4690 y Fe(2)980 4675 y Fk(\002)22 b Fi(C)1149 4690 y Fe(2)1188 4675 y Fo(.)123 4795 y(Its)36 b(unit)f(group)g Fi(U)824 4810 y Fe(12)934 4795 y Fo(is)g(generated)h(b)m(y)h(a)e(30)1803 4759 y Fm(o)1841 4795 y Fo(-rotation)e Fi(\030)40 b Fo(together)35 b(with)h(a)f(rotation-in\015ation)-24 4916 y Fi(\021)47 b Fo(=)189 4840 y Fk(p)p 272 4840 98 4 v 76 x Fi(\032\030)f Fo(where)d Fi(\032)g Fo(=)f(2)28 b(+)1094 4833 y Fk(p)p 1177 4833 49 4 v 83 x Fo(3.)70 b(Note)42 b(the)f(con)m(trast)h(to)f (the)h(eigh)m(t-)f(and)g(tenfold)g(cases)i(where)-24 5036 y(the)k(elemen)m(tary)f(in\015ation)e(w)m(ere)j(pure)g(dilations.) 81 b(The)47 b(full)d(symmetry)i(group)g(therefore)h(is)e(a)-24 5156 y Fl(semidir)-5 b(e)g(ct)37 b Fo(pro)s(duct)g(b)s(et)m(w)m(een)i (the)f(re\015ection)f(group)g Fi(S)43 b Fo(and)38 b(the)f (rotation-in\015ation)d(group)j Fi(U)3654 5171 y Fe(12)3729 5156 y Fo(.)1817 5471 y(14)p eop %%Page: 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2937 1518 V 792 1638 V 868 1602 a(10)p 1039 1638 V 124 w(62+10+10)98 b(150)h(150)g(150)g (150)g(72+12)p 2937 1638 V 794 1641 2146 4 v -24 1807 a(T)-8 b(able)47 b(6:)73 b(Symmetry)47 b(orbit)f(coun)m(ts)j(for)e (LI-classes)h(with)e(\()p Fi(D)2442 1822 y Fe(10)2549 1807 y Fk(\002)33 b Fi(I)8 b Fo(\))47 b(generalized)g(symmetry)-8 b(.)-24 1928 y(If)46 b(m)m(ultiple)e(en)m(tries)i(o)s(ccur)g(in)f(one)h (column,)j(the)d(second)h(refers)g(to)e(orbits)g(con)m(taining)g (mirror)-24 2048 y(symmetric)i(tilings)e(and)i(the)h(third)e(giv)m(es)i (the)f(n)m(um)m(b)s(er)h(of)f(orbits)f(with)h(\()p Fi(I)2968 2012 y Fm(n=)p Fe(2)3118 2048 y Fk(\001)31 b Fi(S)6 b Fo(\)-symmetric)-24 2169 y(tilings.)-24 2562 y(As)35 b(in)e(the)h(ab)s(o)m(v)m(e)g(cases,)i(ev)m(ery)g(tiling)30 b(with)k(a)f(geometric)g(symmetry)h(also)f(sho)m(ws)i(some)f (in\015ation)-24 2682 y(symmetry)-8 b(,)40 b(indicated)d(b)m(y)i(the)f (iden)m(tities)f(\()p Fi(\030)1712 2646 y Fe(3)1777 2682 y Fk(\000)26 b Fo(1\))36 b(=)h(\()p Fi(\030)5 b(\021)29 b Fk(\000)d Fo(1\))p Fi(\030)2517 2646 y Fe(2)2556 2682 y Fi(;)33 b Fo(\()p Fi(\030)2702 2646 y Fe(4)2767 2682 y Fk(\000)26 b Fo(1\))p Fi(\030)3005 2646 y Fe(9)3043 2682 y Fi(\021)41 b Fo(=)36 b Fi(\030)5 b(\021)3344 2646 y Fe(2)3409 2682 y Fk(\000)26 b Fo(1)38 b(and)-24 2802 y(\()p Fi(\030)62 2766 y Fe(6)124 2802 y Fk(\000)23 b Fo(1\))p Fi(\030)359 2766 y Fe(2)398 2802 y Fi(\021)33 b Fo(=)c(\()p Fi(\030)5 b(\021)t Fo(\))760 2766 y Fe(2)821 2802 y Fk(\000)23 b Fo(1.)47 b(The)34 b(symmetry)g(structure)h(of)e (the)h(mirror)d(symmetric)i(tilings)e(can)j(b)s(e)-24 2923 y(read)e(from)f(the)h(maximal)d(real)h(submo)s(dule)i Fn(Z)p Fo([)p Fi(\032)p Fo(])d(whic)m(h)k(corresp)s(onds)g(to)e(the)h (so-called)f(Platin)m(um)-24 3043 y(n)m(um)m(b)s(er)40 b(c)m(hains.)65 b(Tilings)37 b(with)i(one)h(single)e(re\015ection)i (axis)f(split)f(in)m(to)h Fk(\006)p Fi(\032)2909 3007 y Fm(n)2957 3043 y Fo(-orbits.)63 b(Again,)40 b(w)m(e)-24 3163 y(\014nd)33 b(one)g(subtorus)h(for)e(eac)m(h)i(re\015ection)e (axis.)123 3284 y(W)-8 b(e)25 b(illustrate)e(our)i(results)h(with)f (square-triangle)f(tilings.)39 b(The)26 b(precise)g(de\014nition)e(of)h (our)g(class)-24 3404 y(LI[ST])34 b(is)e(giv)m(en)h(in)e(the)i(app)s (endix.)44 b(P)m(atterns)34 b(are)f(constructed)h(through)e(iterated)g (in\015ation.)122 3871 y Fk(\017)48 b Fo(There)37 b(is)f(one)g(single)f (tiling)e(with)220 3991 y(full)i(symmetry)i(\()p Fi(C)963 4006 y Fe(12)1063 3991 y Fk(\002)26 b Fi(I)8 b Fo(\))25 b Fk(\002)1357 4006 y Fm(s)1419 3991 y Fi(S)6 b Fo(.)220 4111 y(It)33 b(is)f(singular)f(in)h(LI[ST].)2240 4382 y @beginspecial 130 @llx 60 @lly 590 @urx 480 @ury 992 @rhi @setspecial %%BeginDocument: st30.eps %!PS-Adobe-3.0 EPSF %%Title: Maple plot %%Creator: MapleV %%Pages: 1 %%BoundingBox: 130 60 590 480 %%DocumentNeededResources: font Courier %%EndComments 20 dict begin gsave /m {moveto} def /l {lineto} def /C {setrgbcolor} def /G {setgray} def /S {stroke} def /NP {newpath} 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2499 m 4997 2053 l 5254 2499 l 4739 2499 l S NP 4550 1795 m 4293 2241 l 4035 1795 l 4550 1795 l S NP 4035 1795 m 4035 1280 l 4550 1280 l 4550 1795 l 4035 1795 l S NP 4550 1795 m 4997 2053 l 4739 2499 l 4293 2241 l 4550 1795 l S NP 4550 1280 m 4997 1538 l 4550 1795 l 4550 1280 l S NP 4997 2053 m 4550 1795 l 4997 1538 l 4997 2053 l S NP 3332 2499 m 3847 2499 l 3589 2945 l 3332 2499 l S NP 4035 3202 m 3589 2945 l 3847 2499 l 4293 2756 l 4035 3202 l S NP 3589 2945 m 4035 3202 l 3589 3460 l 3589 2945 l S NP 3847 2499 m 4293 2241 l 4293 2756 l 3847 2499 l S NP 4739 2499 m 4293 2756 l 4293 2241 l 4739 2499 l S NP 4035 3717 m 3589 3460 l 4035 3202 l 4035 3717 l S NP 4739 2499 m 5254 2499 l 4997 2945 l 4739 2499 l S NP 4035 3717 m 4550 3717 l 4293 4164 l 4035 3717 l S NP 4550 3202 m 4035 3202 l 4293 2756 l 4550 3202 l S NP 4293 2756 m 4739 2499 l 4997 2945 l 4550 3202 l 4293 2756 l S NP 4550 3202 m 4550 3717 l 4035 3717 l 4035 3202 l 4550 3202 l S NP 4997 2945 m 4997 3460 l 4550 3202 l 4997 2945 l S NP 4550 3717 m 4550 3202 l 4997 3460 l 4550 3717 l S boundarythick setlinewidth %%%% The following draws a box around the plot. %%/bd boundarythick 2 idiv def %%[] 0 setdash %%NP bd bd m bd 5000 bd sub l %%6666 bd sub 5000 bd sub l %%6666 bd sub bd l %%bd bd l S showpage grestore end %%Trailer %%EOF %%EndDocument @endspecial 122 4646 a Fk(\017)48 b Fo(There)f(is)e(one)i(orbit)d(con) m(taining)220 4766 y(three)65 b(tilings)c(with)j(\()p Fi(C)1187 4781 y Fe(4)1269 4766 y Fk(\002)44 b Fi(I)51 b Fk(\001)220 4886 y Fi(C)290 4901 y Fe(12)365 4886 y Fo(\))23 b Fk(\002)503 4901 y Fm(s)563 4886 y Fi(S)40 b Fo(symmetry)-8 b(.)48 b(It)34 b(is)g(sin-)220 5007 y(gular)e(in)f(LI[ST].)2240 5217 y @beginspecial 130 @llx 60 @lly 590 @urx 480 @ury 992 @rhi @setspecial %%BeginDocument: st90.eps %!PS-Adobe-3.0 EPSF %%Title: Maple plot %%Creator: MapleV %%Pages: 1 %%BoundingBox: 130 60 590 480 %%DocumentNeededResources: font Courier %%EndComments 20 dict begin gsave /m {moveto} def /l {lineto} def /C {setrgbcolor} def /G {setgray} def /S {stroke} def /NP {newpath} def %%%%This draws a filled polygon and avoids bugs/features %%%% of some postscript interpreters %%%%GHOSTSCRIPT: has a bug in reversepath - removing %%%%the call to reversepath is a sufficient work around /P {gsave fill grestore reversepath stroke} def %%%%This function is needed for drawing text /stringbbox {gsave NP 0 0 m false charpath flattenpath pathbbox 4 2 roll pop pop 1.1 mul cvi exch 1.1 mul cvi exch grestore} def /thin 6 def /medium 10 def /thick 15 def /boundarythick 20 def %% thickness of bounding box %%IncludeResource: font Courier %%576 36 translate %%90 rotate 0.108 0.108 scale 1 setlinejoin 1 setlinecap 0.0 setgray /inch {72 mul} def /fheight 0.35 inch neg def 0 G medium setlinewidth [] 0 setdash NP 4739 1280 m 4739 1795 l 4293 1538 l 4739 1280 l S NP 4739 1795 m 5254 1795 l 4997 2241 l 4739 1795 l S NP 2371 3460 m 1855 3460 l 2113 3014 l 2371 3460 l S NP 1667 2756 m 2113 3014 l 1855 3460 l 1409 3202 l 1667 2756 l S NP 2371 3460 m 2113 3906 l 1855 3460 l 2371 3460 l S NP 2113 3906 m 2371 3460 l 2628 3906 l 2113 3906 l S NP 2628 3906 m 3074 4164 l 2628 4421 l 2628 3906 l 3074 4164 l 2628 4421 l 2628 3906 l S NP 4035 3906 m 4035 4421 l 3589 4164 l 4035 3906 l S NP 2628 3906 m 2371 3460 l 2886 3460 l 2628 3906 l S NP 4035 3906 m 3778 3460 l 4293 3460 l 4035 3906 l S NP 3332 3717 m 3589 4164 l 3074 4164 l 3332 3717 l S NP 3074 4164 m 2628 3906 l 2886 3460 l 3332 3717 l 3074 4164 l S NP 3332 3717 m 3778 3460 l 4035 3906 l 3589 4164 l 3332 3717 l S NP 2886 3460 m 3332 3202 l 3332 3717 l 2886 3460 l S NP 3778 3460 m 3332 3717 l 3332 3202 l 3778 3460 l S NP 4550 3906 m 4035 3906 l 4293 3460 l 4550 3906 l S NP 4035 3906 m 4035 4421 l 3589 4164 l 4035 3906 l S NP 4550 3014 m 4808 3460 l 4293 3460 l 4550 3014 l S NP 5254 3202 m 4808 3460 l 4550 3014 l 4997 2756 l 5254 3202 l S NP 4550 3906 m 4293 3460 l 4808 3460 l 4550 3906 l S NP 2371 1538 m 2371 1022 l 2817 1280 l 2371 1538 l S NP 3074 834 m 2817 1280 l 2371 1022 l 2628 576 l 3074 834 l S NP 2371 1538 m 1924 1280 l 2371 1022 l 2371 1538 l 2371 1022 l 2817 1280 l 2371 1538 l 2817 1280 l 2817 1795 l 2371 1538 l S NP 3074 834 m 2817 1280 l 2371 1022 l 2628 576 l 3074 834 l S NP 3332 1795 m 2817 1795 l 2817 1280 l 3332 1280 l 3332 1795 l S NP 2817 1280 m 3074 834 l 3332 1280 l 2817 1280 l S NP 3332 1280 m 3847 1280 l 3847 1795 l 3332 1795 l 3332 1280 l S NP 3847 1280 m 3332 1280 l 3589 834 l 3847 1280 l S NP 3074 834 m 3589 834 l 3332 1280 l 3074 834 l S NP 4293 1538 m 3847 1280 l 4293 1022 l 4293 1538 l S NP 4035 576 m 4293 1022 l 3847 1280 l 3589 834 l 4035 576 l S NP 4293 1538 m 3847 1795 l 3847 1280 l 4293 1538 l S NP 4035 576 m 4293 1022 l 3847 1280 l 3589 834 l 4035 576 l S NP 4293 1538 m 3847 1280 l 4293 1022 l 4293 1538 l 4293 1022 l 4739 1280 l 4293 1538 l S NP 2371 3460 m 1855 3460 l 2113 3014 l 2371 3460 l 2113 3014 l 2628 3014 l 2371 3460 l S NP 1667 2756 m 2113 3014 l 1855 3460 l 1409 3202 l 1667 2756 l S NP 2628 2499 m 2628 3014 l 2113 3014 l 2113 2499 l 2628 2499 l S NP 2113 3014 m 1667 2756 l 2113 2499 l 2113 3014 l S NP 2628 2499 m 2113 2499 l 2371 2053 l 2628 2499 l S NP 1667 2241 m 2113 2499 l 1667 2756 l 1667 2241 l S NP 2371 2053 m 1924 1795 l 2371 1538 l 2371 2053 l S NP 1924 1795 m 1667 2241 l 1409 1795 l 1924 1795 l S NP 1667 2241 m 1924 1795 l 2371 2053 l 2113 2499 l 1667 2241 l S NP 4293 3460 m 4035 3014 l 4550 3014 l 4293 3460 l 4550 3014 l 4808 3460 l 4293 3460 l S NP 4550 2499 m 4550 3014 l 4035 3014 l 4035 2499 l 4550 2499 l S NP 5254 3202 m 4808 3460 l 4550 3014 l 4997 2756 l 5254 3202 l S NP 4550 3014 m 4550 2499 l 4997 2756 l 4550 3014 l S NP 4035 2499 m 4293 2053 l 4550 2499 l 4035 2499 l S NP 4997 2241 m 4997 2756 l 4550 2499 l 4997 2241 l S NP 4293 2053 m 4293 1538 l 4739 1795 l 4293 2053 l S NP 4739 1795 m 5254 1795 l 4997 2241 l 4739 1795 l S NP 4550 2499 m 4293 2053 l 4739 1795 l 4997 2241 l 4550 2499 l S NP 4293 1538 m 3847 1795 l 3847 1280 l 4293 1538 l S NP 3332 1280 m 3847 1280 l 3847 1795 l 3332 1795 l 3332 1280 l S NP 3332 1795 m 2817 1795 l 2817 1280 l 3332 1280 l 3332 1795 l S NP 2371 1538 m 2817 1280 l 2817 1795 l 2371 1538 l S NP 4293 1538 m 4293 2053 l 3847 1795 l 4293 1538 l S NP 2371 1538 m 2817 1795 l 2371 2053 l 2371 1538 l S NP 2628 3014 m 2628 2499 l 3074 2756 l 2628 3014 l S NP 2628 2499 m 2628 3014 l 2113 3014 l 2113 2499 l 2628 2499 l S NP 4550 3014 m 4293 3460 l 4035 3014 l 4550 3014 l S NP 4293 3460 m 3778 3460 l 4035 3014 l 4293 3460 l S NP 3589 2241 m 3847 1795 l 4293 2053 l 4035 2499 l 3589 2241 l S NP 3847 1795 m 3589 2241 l 3332 1795 l 3847 1795 l S NP 3332 1795 m 3589 2241 l 3074 2241 l 3332 1795 l S NP 2817 1795 m 3332 1795 l 3074 2241 l 2817 1795 l S NP 2628 2499 m 2371 2053 l 2817 1795 l 3074 2241 l 2628 2499 l S NP 4293 2053 m 4550 2499 l 4035 2499 l 4293 2053 l S NP 3589 2756 m 4035 3014 l 3778 3460 l 3332 3202 l 3589 2756 l 3332 3202 l 3074 2756 l 3589 2756 l S NP 3332 3202 m 2886 3460 l 2628 3014 l 3074 2756 l 3332 3202 l S NP 2371 3460 m 2628 3014 l 2886 3460 l 2371 3460 l S NP 2371 2053 m 2628 2499 l 2113 2499 l 2371 2053 l S NP 3589 2241 m 4035 2499 l 3589 2756 l 3589 2241 l S NP 3074 2241 m 3074 2756 l 2628 2499 l 3074 2241 l S NP 3074 2756 m 3074 2241 l 3589 2241 l 3589 2756 l 3074 2756 l S NP 4550 2499 m 4550 3014 l 4035 3014 l 4035 2499 l 4550 2499 l S NP 4035 3014 m 3589 2756 l 4035 2499 l 4035 3014 l S NP 2371 3460 m 2113 3014 l 2628 3014 l 2371 3460 l S NP 3778 3460 m 3332 3717 l 3332 3202 l 3778 3460 l S NP 2886 3460 m 3332 3202 l 3332 3717 l 2886 3460 l S NP 1924 1280 m 2371 1538 l 1924 1795 l 1924 1280 l S NP 1924 1795 m 1667 2241 l 1409 1795 l 1924 1795 l S boundarythick setlinewidth %%%% The following draws a box around the plot. %%/bd boundarythick 2 idiv def %%[] 0 setdash %%NP bd bd m bd 5000 bd sub l %%6666 bd sub 5000 bd sub l %%6666 bd sub bd l %%bd bd l S showpage grestore end %%Trailer %%EOF %%EndDocument @endspecial 1817 5471 a(15)p eop %%Page: 16 16 16 15 bop 122 562 a Fk(\017)48 b Fo(There)69 b(is)e(one)h(orbit)e(of)h (eigh)m(t)220 683 y(tilings)26 b(with)i(\()p Fi(C)835 698 y Fe(3)887 683 y Fk(\002)13 b Fi(I)1028 646 y Fe(2)1082 683 y Fk(\001)g Fi(C)1193 698 y Fe(12)1267 683 y Fo(\))g Fk(\002)1395 698 y Fm(s)1446 683 y Fi(S)220 803 y Fo(symmetry)-8 b(.)113 b(The)56 b(mem)m(b)s(ers)f(of)220 923 y(LI[ST])34 b(are)e(regular.)1597 1134 y @beginspecial 130 @llx 60 @lly 590 @urx 480 @ury 992 @rhi @setspecial %%BeginDocument: st1201.eps %!PS-Adobe-3.0 EPSF %%Title: Maple plot %%Creator: MapleV %%Pages: 1 %%BoundingBox: 130 60 590 480 %%DocumentNeededResources: font Courier %%EndComments 20 dict begin gsave /m {moveto} def /l {lineto} def /C {setrgbcolor} def /G {setgray} def /S {stroke} def /NP {newpath} def %%%%This draws a filled polygon and avoids bugs/features %%%% of some postscript interpreters %%%%GHOSTSCRIPT: has a bug in reversepath - removing %%%%the call to reversepath is a sufficient work around /P {gsave fill grestore reversepath stroke} def %%%%This function is needed for drawing text /stringbbox {gsave NP 0 0 m false charpath flattenpath pathbbox 4 2 roll pop pop 1.1 mul cvi exch 1.1 mul cvi exch grestore} def /thin 6 def /medium 10 def /thick 15 def /boundarythick 20 def %% thickness of bounding box %%IncludeResource: font Courier %%576 36 translate %%90 rotate 0.108 0.108 scale 1 setlinejoin 1 setlinecap 0.0 setgray /inch {72 mul} def /fheight 0.35 inch neg def 0 G medium setlinewidth [] 0 setdash NP 4362 3115 m 3884 3391 l 3884 2839 l 4362 3115 l S NP 3332 2839 m 3884 2839 l 3884 3391 l 3332 3391 l 3332 2839 l S NP 3332 3391 m 2780 3391 l 2780 2839 l 3332 2839 l 3332 3391 l S NP 2301 3115 m 2780 2839 l 2780 3391 l 2301 3115 l S NP 4362 3115 m 4362 3667 l 3884 3391 l 4362 3115 l S NP 2301 3115 m 2780 3391 l 2301 3667 l 2301 3115 l S NP 3608 3869 m 3884 3391 l 4362 3667 l 4086 4145 l 3608 3869 l S NP 3884 3391 m 3608 3869 l 3332 3391 l 3884 3391 l S NP 3332 3391 m 3608 3869 l 3056 3869 l 3332 3391 l S NP 2780 3391 m 3332 3391 l 3056 3869 l 2780 3391 l S NP 2578 4145 m 2301 3667 l 2780 3391 l 3056 3869 l 2578 4145 l S NP 4362 3667 m 4638 4145 l 4086 4145 l 4362 3667 l S NP 2301 3667 m 2578 4145 l 2025 4145 l 2301 3667 l S NP 3608 3869 m 4086 4145 l 3608 4421 l 3608 3869 l S NP 3056 3869 m 3056 4421 l 2578 4145 l 3056 3869 l S NP 3056 4421 m 3056 3869 l 3608 3869 l 3608 4421 l 3056 4421 l S NP 4086 4145 m 4362 3667 l 4638 4145 l 4086 4145 l S NP 4362 3667 m 4362 3115 l 4840 3391 l 4362 3667 l S NP 2578 4145 m 2025 4145 l 2301 3667 l 2578 4145 l S NP 2301 3667 m 1823 3391 l 2301 3115 l 2301 3667 l S NP 1547 2361 m 1823 2839 l 1271 2839 l 1547 2361 l S NP 1823 2839 m 2301 3115 l 1823 3391 l 1823 2839 l S NP 5116 2361 m 5392 2839 l 4840 2839 l 5116 2361 l S NP 4840 2839 m 4840 3391 l 4362 3115 l 4840 2839 l S NP 3332 1331 m 3810 1607 l 3332 1883 l 3332 1331 l 3332 1883 l 2854 1607 l 3332 1331 l S NP 3608 2361 m 3332 1883 l 3810 1607 l 4086 2085 l 3608 2361 l S NP 2578 2085 m 2854 1607 l 3332 1883 l 3056 2361 l 2578 2085 l S NP 3332 1883 m 3608 2361 l 3056 2361 l 3332 1883 l S NP 4086 2085 m 4362 2563 l 3884 2839 l 3608 2361 l 4086 2085 l S NP 3056 2361 m 2780 2839 l 2301 2563 l 2578 2085 l 3056 2361 l S NP 3884 2839 m 3332 2839 l 3608 2361 l 3884 2839 l S NP 2780 2839 m 3056 2361 l 3332 2839 l 2780 2839 l S NP 3608 2361 m 3332 2839 l 3056 2361 l 3608 2361 l S NP 4362 3115 m 3884 3391 l 3884 2839 l 4362 3115 l S NP 2301 3115 m 2780 2839 l 2780 3391 l 2301 3115 l S NP 3332 2839 m 3884 2839 l 3884 3391 l 3332 3391 l 3332 2839 l S NP 3332 3391 m 2780 3391 l 2780 2839 l 3332 2839 l 3332 3391 l S NP 4362 3115 m 3884 2839 l 4362 2563 l 4362 3115 l S NP 2301 3115 m 2301 2563 l 2780 2839 l 2301 3115 l 2301 2563 l 2780 2839 l 2301 3115 l S NP 3056 2361 m 2780 2839 l 2301 2563 l 2578 2085 l 3056 2361 l S NP 2578 2085 m 2854 1607 l 3332 1883 l 3056 2361 l 2578 2085 l S NP 3332 1331 m 3332 1883 l 2854 1607 l 3332 1331 l S NP 2301 3115 m 1823 2839 l 2301 2563 l 2301 3115 l S NP 3332 1331 m 2854 1607 l 2854 1055 l 3332 1331 l S NP 2025 2085 m 2301 2563 l 1823 2839 l 1547 2361 l 2025 2085 l S NP 2301 2563 m 2025 2085 l 2578 2085 l 2301 2563 l S NP 2578 2085 m 2025 2085 l 2301 1607 l 2578 2085 l S NP 2854 1607 m 2578 2085 l 2301 1607 l 2854 1607 l S NP 2301 1055 m 2854 1055 l 2854 1607 l 2301 1607 l 2301 1055 l S NP 1823 2839 m 1271 2839 l 1547 2361 l 1823 2839 l S NP 2854 1055 m 2301 1055 l 2578 576 l 2854 1055 l S NP 2025 2085 m 1547 2361 l 1547 1809 l 2025 2085 l S NP 2301 1607 m 1823 1331 l 2301 1055 l 2301 1607 l S NP 1823 1331 m 2301 1607 l 2025 2085 l 1547 1809 l 1823 1331 l S NP 3332 1331 m 3810 1607 l 3332 1883 l 3332 1331 l S NP 3608 2361 m 3332 1883 l 3810 1607 l 4086 2085 l 3608 2361 l S NP 4086 2085 m 4362 2563 l 3884 2839 l 3608 2361 l 4086 2085 l S NP 4362 3115 m 3884 2839 l 4362 2563 l 4362 3115 l S NP 3332 1331 m 3810 1055 l 3810 1607 l 3332 1331 l S NP 4362 3115 m 4362 2563 l 4840 2839 l 4362 3115 l S NP 4362 1607 m 3810 1607 l 3810 1055 l 4362 1055 l 4362 1607 l S NP 3810 1607 m 4362 1607 l 4086 2085 l 3810 1607 l S NP 4086 2085 m 4362 1607 l 4638 2085 l 4086 2085 l S NP 4362 2563 m 4086 2085 l 4638 2085 l 4362 2563 l S NP 5116 2361 m 4840 2839 l 4362 2563 l 4638 2085 l 5116 2361 l S NP 3810 1055 m 4086 576 l 4362 1055 l 3810 1055 l S NP 4840 2839 m 5116 2361 l 5392 2839 l 4840 2839 l S NP 4362 1607 m 4362 1055 l 4840 1331 l 4362 1607 l S NP 4638 2085 m 5116 1809 l 5116 2361 l 4638 2085 l S NP 5116 1809 m 4638 2085 l 4362 1607 l 4840 1331 l 5116 1809 l S NP 2301 1055 m 2578 576 l 2854 1055 l 2301 1055 l S NP 2854 1055 m 3332 778 l 3332 1331 l 2854 1055 l S NP 4362 1055 m 3810 1055 l 4086 576 l 4362 1055 l S NP 3810 1055 m 3332 1331 l 3332 778 l 3810 1055 l S boundarythick setlinewidth %%%% The following draws a box around the plot. %%/bd boundarythick 2 idiv def %%[] 0 setdash %%NP bd bd m bd 5000 bd sub l %%6666 bd sub 5000 bd sub l %%6666 bd sub bd l %%bd bd l S showpage grestore end %%Trailer %%EOF %%EndDocument @endspecial 1096 w @beginspecial 130 @llx 60 @lly 590 @urx 480 @ury 992 @rhi @setspecial %%BeginDocument: st1202.eps %!PS-Adobe-3.0 EPSF %%Title: Maple plot %%Creator: MapleV %%Pages: 1 %%BoundingBox: 130 60 590 480 %%DocumentNeededResources: font Courier %%EndComments 20 dict begin gsave /m {moveto} def /l {lineto} def /C {setrgbcolor} def /G {setgray} def /S {stroke} def /NP {newpath} def %%%%This draws a filled polygon and avoids bugs/features %%%% of some postscript interpreters %%%%GHOSTSCRIPT: has a bug in reversepath - removing %%%%the call to reversepath is a sufficient work around /P {gsave fill grestore reversepath stroke} def %%%%This function is needed for drawing text /stringbbox {gsave NP 0 0 m false charpath flattenpath pathbbox 4 2 roll pop pop 1.1 mul cvi exch 1.1 mul cvi exch grestore} def /thin 6 def /medium 10 def /thick 15 def /boundarythick 20 def %% thickness of bounding box %%IncludeResource: font Courier %%576 36 translate %%90 rotate 0.108 0.108 scale 1 setlinejoin 1 setlinecap 0.0 setgray /inch {72 mul} def /fheight 0.35 inch neg def 0 G medium setlinewidth [] 0 setdash NP 2353 2988 m 2091 3442 l 1828 2988 l 2353 2988 l 2615 3442 l 2091 3442 l 2353 2988 l S NP 2091 3967 m 2091 3442 l 2615 3442 l 2615 3967 l 2091 3967 l S NP 2615 3442 m 3069 3705 l 2615 3967 l 2615 3442 l S NP 3069 3705 m 3332 4159 l 2877 4421 l 2615 3967 l 3069 3705 l S NP 4310 2988 m 4835 2988 l 4573 3442 l 4310 2988 l 4573 3442 l 4048 3442 l 4310 2988 l S NP 4048 3967 m 3786 4421 l 3332 4159 l 3594 3705 l 4048 3967 l 4048 3442 l 4573 3442 l 4573 3967 l 4048 3967 l S NP 4048 3442 m 4048 3967 l 3594 3705 l 4048 3442 l S NP 3069 3705 m 3332 4159 l 2877 4421 l 2615 3967 l 3069 3705 l S NP 4048 3967 m 3786 4421 l 3332 4159 l 3594 3705 l 4048 3967 l S NP 3332 4159 m 3069 3705 l 3594 3705 l 3332 4159 l S NP 2615 3967 m 2615 3442 l 3069 3705 l 2615 3967 l S NP 4048 3967 m 3594 3705 l 4048 3442 l 4048 3967 l S NP 3332 3250 m 3594 3705 l 3069 3705 l 3332 3250 l S NP 2615 3442 m 2353 2988 l 2877 2988 l 2615 3442 l S NP 4048 3442 m 3786 2988 l 4310 2988 l 4048 3442 l S NP 2877 2988 m 3332 2726 l 3332 3250 l 2877 2988 l S NP 3786 2988 m 3332 3250 l 3332 2726 l 3786 2988 l S NP 3069 3705 m 2615 3442 l 2877 2988 l 3332 3250 l 3069 3705 l S NP 3332 3250 m 3786 2988 l 4048 3442 l 3594 3705 l 3332 3250 l S NP 2353 2988 m 2091 3442 l 1828 2988 l 2353 2988 l 1828 2988 l 2091 2534 l 2353 2988 l S NP 1636 2272 m 1374 1817 l 1828 1555 l 2091 2009 l 1636 2272 l 2091 2534 l 1828 2988 l 1374 2726 l 1636 2272 l S NP 2091 2534 m 1636 2272 l 2091 2009 l 2091 2534 l S NP 4310 2988 m 4835 2988 l 4573 3442 l 4310 2988 l 4573 2534 l 4835 2988 l 4310 2988 l S NP 5289 2726 m 4835 2988 l 4573 2534 l 5027 2272 l 5289 2726 l S NP 4573 2534 m 4573 2009 l 5027 2272 l 4573 2534 l S NP 4573 2009 m 4835 1555 l 5289 1817 l 5027 2272 l 4573 2009 l S NP 2353 1555 m 1828 1555 l 1828 1031 l 2353 1031 l 2353 1555 l S NP 1636 2272 m 1374 1817 l 1828 1555 l 2091 2009 l 1636 2272 l S NP 1828 1555 m 2353 1555 l 2091 2009 l 1828 1555 l S NP 2353 1031 m 2807 1293 l 2353 1555 l 2353 1031 l S NP 1636 2272 m 2091 2009 l 2091 2534 l 1636 2272 l S NP 2615 2009 m 2091 2009 l 2353 1555 l 2615 2009 l S NP 2807 1293 m 3332 1293 l 3069 1747 l 2807 1293 l S NP 2091 2534 m 2615 2534 l 2353 2988 l 2091 2534 l S NP 3069 1747 m 3069 2272 l 2615 2009 l 3069 1747 l S NP 2615 2534 m 2615 2009 l 3069 2272 l 2615 2534 l S NP 2353 1555 m 2807 1293 l 3069 1747 l 2615 2009 l 2353 1555 l S NP 2615 2009 m 2615 2534 l 2091 2534 l 2091 2009 l 2615 2009 l S NP 4573 2009 m 4835 1555 l 5289 1817 l 5027 2272 l 4573 2009 l S NP 4310 1031 m 4835 1031 l 4835 1555 l 4310 1555 l 4310 1031 l S NP 4835 1555 m 4573 2009 l 4310 1555 l 4835 1555 l S NP 5027 2272 m 4573 2534 l 4573 2009 l 5027 2272 l S NP 4310 1031 m 4310 1555 l 3856 1293 l 4310 1031 l S NP 4048 2009 m 4310 1555 l 4573 2009 l 4048 2009 l S NP 4573 2534 m 4310 2988 l 4048 2534 l 4573 2534 l S NP 3856 1293 m 3594 1747 l 3332 1293 l 3856 1293 l S NP 4048 2534 m 3594 2272 l 4048 2009 l 4048 2534 l S NP 3594 1747 m 4048 2009 l 3594 2272 l 3594 1747 l S NP 4573 2009 m 4573 2534 l 4048 2534 l 4048 2009 l 4573 2009 l S NP 4048 2009 m 3594 1747 l 3856 1293 l 4310 1555 l 4048 2009 l S NP 2353 2988 m 2615 2534 l 2877 2988 l 2353 2988 l S NP 3332 2726 m 2877 2988 l 2615 2534 l 3069 2272 l 3332 2726 l S NP 2877 2988 m 3332 2726 l 3332 3250 l 2877 2988 l S NP 2615 2534 m 2615 2009 l 3069 2272 l 2615 2534 l S NP 3069 1747 m 3069 2272 l 2615 2009 l 3069 1747 l S NP 3786 2988 m 3332 3250 l 3332 2726 l 3786 2988 l S NP 3069 1747 m 3332 1293 l 3594 1747 l 3069 1747 l S NP 3786 2988 m 4048 2534 l 4310 2988 l 3786 2988 l S NP 3594 2272 m 3332 2726 l 3069 2272 l 3594 2272 l S NP 3069 2272 m 3069 1747 l 3594 1747 l 3594 2272 l 3069 2272 l S NP 3594 2272 m 4048 2534 l 3786 2988 l 3332 2726 l 3594 2272 l S NP 3594 1747 m 4048 2009 l 3594 2272 l 3594 1747 l S NP 4048 2534 m 3594 2272 l 4048 2009 l 4048 2534 l S NP 3332 1293 m 3069 839 l 3594 839 l 3332 1293 l 2807 1293 l 3069 839 l 3332 1293 l S NP 2615 576 m 3069 839 l 2807 1293 l 2353 1031 l 2615 576 l S NP 2807 1293 m 2353 1555 l 2353 1031 l 2807 1293 l S NP 2353 1555 m 1828 1555 l 1828 1031 l 2353 1031 l 2353 1555 l S NP 3332 1293 m 3069 839 l 3594 839 l 3332 1293 l 3594 839 l 3856 1293 l 3332 1293 l S NP 4310 1031 m 4835 1031 l 4835 1555 l 4310 1555 l 4310 1031 l 3856 1293 l 3594 839 l 4048 576 l 4310 1031 l S NP 3856 1293 m 4310 1031 l 4310 1555 l 3856 1293 l S boundarythick setlinewidth %%%% The following draws a box around the plot. %%/bd boundarythick 2 idiv def %%[] 0 setdash %%NP bd bd m bd 5000 bd sub l %%6666 bd sub 5000 bd sub l %%6666 bd sub bd l %%bd bd l S showpage grestore end %%Trailer %%EOF %%EndDocument @endspecial 122 1279 a Fk(\017)48 b Fo(Finally)-8 b(,)53 b(there)f(is)f(one)g(orbit)f(of)220 1399 y(t)m(w)m(elv)m(e)e(tilings)c (with)i(\()p Fi(C)1183 1414 y Fe(2)1253 1399 y Fk(\002)32 b Fi(I)1413 1363 y Fe(2)1484 1399 y Fk(\001)220 1520 y Fi(C)290 1535 y Fe(6)329 1520 y Fo(\))s Fk(\002)447 1535 y Fm(s)488 1520 y Fi(S)d Fo(symmetry)-8 b(.)41 b(The)24 b(tilings)220 1640 y(in)32 b(are)h(regular)e(in)h(LI[ST].)1597 1733 y @beginspecial 80 @llx 100 @lly 630 @urx 430 @ury 708 @rhi @setspecial %%BeginDocument: st1801.eps %!PS-Adobe-3.0 EPSF %%Title: Maple plot %%Creator: MapleV %%Pages: 1 %%BoundingBox: 80 100 630 430 %%DocumentNeededResources: font Courier %%EndComments 20 dict begin gsave /m {moveto} def /l {lineto} def /C {setrgbcolor} def /G {setgray} def /S {stroke} def /NP {newpath} def %%%%This draws a filled polygon and avoids bugs/features %%%% of some postscript interpreters %%%%GHOSTSCRIPT: has a bug in reversepath - removing %%%%the call to reversepath is a sufficient work around /P {gsave fill grestore reversepath stroke} def %%%%This function is needed for drawing text /stringbbox {gsave NP 0 0 m false charpath flattenpath pathbbox 4 2 roll pop pop 1.1 mul cvi exch 1.1 mul cvi exch grestore} def /thin 6 def /medium 10 def /thick 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5592 3629 l S NP 3937 3629 m 4462 3326 l 4462 3932 l 3937 3629 l S NP 4159 2196 m 4462 1672 l 4764 2196 l 4159 2196 l S NP 4159 2802 m 4764 2802 l 4462 3326 l 4159 2802 l S NP 4764 2802 m 4159 2802 l 4159 2196 l 4764 2196 l 4764 2802 l S NP 4462 1066 m 5067 1066 l 5067 1672 l 4462 1672 l 4462 1066 l S NP 5067 1672 m 4764 2196 l 4462 1672 l 5067 1672 l S NP 5592 3629 m 5067 3932 l 5067 3326 l 5592 3629 l S NP 5592 1974 m 5894 2499 l 5289 2499 l 5592 1974 l S NP 5592 3023 m 5289 2499 l 5894 2499 l 5592 3023 l S boundarythick setlinewidth %%%% The following draws a box around the plot. %%/bd boundarythick 2 idiv def %%[] 0 setdash %%NP bd bd m bd 5000 bd sub l %%6666 bd sub 5000 bd sub l %%6666 bd sub bd l %%bd bd l S showpage grestore end %%Trailer %%EOF %%EndDocument @endspecial 2693 1674 a @beginspecial 80 @llx 100 @lly 630 @urx 430 @ury 566 @rhi @setspecial %%BeginDocument: st1802.eps %!PS-Adobe-3.0 EPSF %%Title: Maple plot %%Creator: MapleV %%Pages: 1 %%BoundingBox: 80 100 630 430 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l S NP 4018 1416 m 3331 1812 l 3331 1019 l 4018 1416 l S NP 3728 2499 m 4415 2102 l 4415 2895 l 3728 2499 l S NP 4415 2895 m 4018 3582 l 3331 3186 l 3728 2499 l 4415 2895 l S NP 3728 2499 m 3331 1812 l 4018 1416 l 4415 2102 l 3728 2499 l S NP 3331 3186 m 2935 2499 l 3728 2499 l 3331 3186 l S NP 3331 1812 m 3728 2499 l 2935 2499 l 3331 1812 l S boundarythick setlinewidth %%%% The following draws a box around the plot. %%/bd boundarythick 2 idiv def %%[] 0 setdash %%NP bd bd m bd 5000 bd sub l %%6666 bd sub 5000 bd sub l %%6666 bd sub bd l %%bd bd l S showpage grestore end %%Trailer %%EOF %%EndDocument @endspecial 122 1915 a Fk(\017)48 b Fo(The)34 b(orbit)d(structure)j (for)e(tilings)e(without)i(rotational)e(symmetry)j(is)f(sho)m(wn)i(in)e (T)-8 b(ab.)33 b(7.)p -19 2166 3771 4 v -21 2287 4 121 v 10 2250 a Fi(c)52 2265 y Fm(n;k)p 171 2287 V 275 2250 a Fo(0)276 b(1)j(2)222 b(3)187 b(4)i(5)h(6)362 b(7)355 b(8)306 b(9)200 b(10)149 b(11)p 3750 2287 V -19 2290 3771 4 v -21 2410 4 121 v 59 2374 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59 3217 a(8)p 171 3253 V 118 w(392)178 b(392)94 b(372+24)37 b(392)89 b(392)i(392)h(384)265 b(392)83 b(338+21+21)33 b(392)127 b(384)100 b(392)p 3750 3253 V -21 3373 V 59 3337 a(9)p 171 3373 V 94 w(1299)129 b(1309)j(1309)75 b(1299)39 b(1309)k(1292)f(1299)216 b(1292)208 b(1292)159 b(1299)78 b(1292)50 b(1309)p 3750 3373 V -21 3494 V 34 3458 a(10)p 171 3494 V 70 w(4356)42 b(4320+72)j(4356)75 b(4380)39 b(4356)k(4356)f(4356)h(4200+72+72)33 b(4356)159 b(4356)78 b(4356)50 b(4380)p 3750 3494 V -19 3497 3771 4 v -24 3709 a(T)-8 b(able)31 b(7:)42 b(Symmetry)31 b(orbit)f(coun)m (ts)i(for)e(LI-classes)h(with)g(\()p Fi(C)2286 3724 y Fe(12)2379 3709 y Fk(\002)19 b Fi(I)8 b Fo(\))18 b Fk(\002)2659 3724 y Fm(s)2715 3709 y Fi(S)36 b Fo(generalized)31 b(symmetry)-8 b(.)-24 3829 y(In)44 b(columns)e(with)g(sev)m(eral)i(en)m(tries,)i(the) d(second)h(corresp)s(onds)g(to)e(orbits)h(of)f(mirror)f(symmetric)-24 3950 y(tilings,)31 b(the)i(third)f(en)m(try)h(corresp)s(onds)h(to)e (orbits)g(with)h Fi(I)2168 3899 y 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b(there)f(are)g(t)m(w)m (o)g(or)f(more)f(indep)s(enden)m(t)j(in\015ation)d(scales)h(for)g (LI-classes)1817 5471 y(16)p eop %%Page: 17 17 17 16 bop -24 407 a Fo(with)30 b(higher)g(rotational)d(symmetry)k([11)o (].)43 b(This)30 b(corresp)s(onds)i(to)e(the)g(fact)g(that)g(in)f(the)i (pro)5 b(jection)-24 527 y(picture)33 b(w)m(e)h(need)f(to)f(start)h (with)f(an)h(em)m(b)s(edding)f(lattice)f(of)h(dimension)f(higher)h (than)h(four.)123 648 y(Here,)26 b(w)m(e)g(shortly)e(presen)m(t)i(ho)m (w)f(to)e(deal)h(with)g(these)h(cases)h(within)d(the)i(torus)f (parametrization.)-24 768 y(The)31 b(case)f(of)f(LI-classes)i(with)e Fi(D)1222 783 y Fe(14)1312 768 y Fk(\002)16 b Fi(I)1448 783 y Fe(1)1504 768 y Fk(\002)g Fi(I)1640 783 y Fe(2)1710 768 y Fo(generalized)29 b(symmetry)h(shall)e(serv)m(e)j(as)f(an)f (example.)123 888 y(The)37 b(unit)e(group)h(of)g(the)g(cyclotomic)f (\014eld)h Fn(Q)11 b Fo(\()p Fi(\030)5 b Fo(\),)42 b Fi(\030)c Fo(=)c(exp)q(\()p Fi(\031)t(i=)p Fo(7\),)i(is)g(generated)h 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b(their)g(complex)f(conjugates.)75 b(Its)43 b(Galois)d(group)j(is)f(cyclic:)64 b Fk(G)51 b(')46 b Fi(C)3690 1264 y Fe(6)3729 1249 y Fo(,)-24 1370 y(the)40 b(same)f(as)g(that)g(of)g Fi(P)927 1385 y Fe(7)966 1370 y Fo(\()p Fi(x)p Fo(\))h(=)e Fi(P)1314 1385 y Fe(14)1389 1370 y Fo(\()p Fk(\000)p Fi(x)p Fo(\).)64 b(\(Hence)41 b(6)d(is)h(also)f(the)i(minim)m(um)c(dimension)i(of)g(the)-24 1490 y(em)m(b)s(edding)d(lattice\).)49 b(The)36 b(total)d(n)m(um)m(b)s (ers)j(of)f(symmetric)f(tilings)e(are)j(then)h(giv)m(en)f(again)f(b)m (y)h(the)-24 1611 y(corresp)s(onding)f Fi(N)682 1626 y Fe(6)721 1611 y Fo(-norms)f(as)h(in)f(\(14\).)46 b(Multiple)32 b(symmetries)h(for)g(sp)s(ecial)g(tilings)e(are)j(indicated)-24 1731 y(through)f(iden)m(tities)e(within)h Fn(Q)11 b Fo(\()p Fi(\030)5 b Fo(\))38 b(lik)m(e)32 b(in)g(the)h(cases)h(discussed)g(ab)s (o)m(v)m(e.)123 1851 y(Here,)f(w)m(e)h(giv)m(e)e(a)h(classi\014cation)e (of)h(all)e(tilings)g(with)j(non)m(trivial)d(rotation)h(symmetry)-8 b(.)122 2080 y 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rotate n 0 0 7 7 0 360 DrawEllipse gs col0 s gr gr % Rotated Ellipse gs 573 523 translate -90.012 rotate n 0 0 7 7 0 360 DrawEllipse gs col0 s gr gr % Rotated Ellipse gs 465 523 translate -90.012 rotate n 0 0 7 7 0 360 DrawEllipse gs col0 s gr gr % Rotated Ellipse gs 1219 259 translate -300.001 rotate n 0 0 7 7 0 360 DrawEllipse gs 0.00 setgray fill gr gs col0 s gr gr % Rotated Ellipse gs 1134 309 translate -300.001 rotate n 0 0 7 7 0 360 DrawEllipse gs 0.00 setgray fill gr gs col0 s gr gr % Rotated Ellipse gs 1099 309 translate -59.989 rotate n 0 0 7 7 0 360 DrawEllipse gs 0.00 setgray fill gr gs col0 s gr gr % Rotated Ellipse gs 1021 256 translate -59.989 rotate n 0 0 7 7 0 360 DrawEllipse gs 0.00 setgray fill gr gs col0 s gr gr % Polyline n 1275 615 m 1275 775 l 1115 775 l 1115 615 l clp gs col0 s gr % Polyline n 955 615 m 955 775 l 1115 775 l 1115 615 l clp gs col0 s gr % Polyline n 896 396 m 1035 476 l 1115 338 l 975 258 l clp gs col0 s gr % Polyline n 1035 476 m 896 396 l 816 534 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504 l gs col0 s gr % Polyline n 1212 453 m 1197 427 l gs col0 s gr % Polyline n 1319 426 m 1334 452 l gs col0 s gr % Polyline n 1300 397 m 1285 371 l gs col0 s gr % Polyline n 1085 355 m 1059 340 l gs col0 s gr % Polyline n 976 293 m 1002 308 l gs col0 s gr % Polyline n 1141 356 m 1167 341 l gs col0 s gr % Polyline n 1254 296 m 1228 311 l gs col0 s gr % Polyline n 1249 763 m 1249 733 l gs col0 s gr % Polyline n 984 755 m 984 725 l gs col0 s gr [5.000000] 0 setdash % Polyline n 1117 180 m 815 695 l clp gs col-1 s gr [] 0 setdash [5.000000] 0 setdash % Polyline n 815 695 m 1417 695 l 1417 694 l clp gs col-1 s gr [] 0 setdash [5.000000] 0 setdash % Polyline n 1417 694 m 1116 180 l clp gs col-1 s gr [] 0 setdash % Open spline n 1276.000 615.000 m 1346.500 655.500 l 1417.000 696.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 1415.000 696.000 m 1415.000 615.500 l 1415.000 535.000 l gs col0 s gr % Open spline n 1275.000 775.000 m 1344.500 735.000 l 1414.000 695.000 l gs col0 s gr % Open spline n 1196.000 476.000 m 1155.500 545.500 l 1115.000 615.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 1115.000 615.000 m 1155.500 545.500 l 1196.000 476.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 1115.000 615.000 m 1074.500 545.500 l 1034.000 476.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 1035.000 476.000 m 1115.000 476.000 l 1195.000 476.000 l gs col0 s gr % Open spline n 1034.000 476.000 m 1074.500 545.500 l 1115.000 615.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 816.000 534.000 m 815.500 614.500 l 815.000 695.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 955.000 775.000 m 885.500 735.000 l 816.000 695.000 l gs col0 s gr % Open spline n 1035.000 476.000 m 1115.000 476.000 l 1195.000 476.000 l gs col0 s gr % Open spline n 1116.000 179.000 m 1045.500 218.500 l 975.000 258.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 1115.000 179.000 m 1185.500 218.500 l 1256.000 258.000 l gs 0.00 setgray 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554 l gs col-1 s gr n 513.000 539.000 m 543.000 554.000 l 513.000 569.000 l gs 2 setlinejoin col-1 s gr % Polyline n 811 376 m 785 361 l gs col0 s gr % Polyline n 703 312 m 729 327 l gs col0 s gr % Polyline n 651 419 m 666 393 l gs col0 s gr % Polyline n 740 474 m 755 448 l gs col0 s gr % Polyline n 1023 419 m 1008 393 l gs col0 s gr % Polyline n 933 475 m 918 449 l gs col0 s gr % Polyline n 742 522 m 757 548 l gs col0 s gr % Polyline n 649 576 m 664 602 l gs col0 s gr % Polyline n 805 628 m 779 643 l gs col0 s gr % Polyline n 716 696 m 701 670 l gs col0 s gr % Polyline n 864 623 m 890 638 l gs col0 s gr % Polyline n 960 694 m 975 668 l gs col0 s gr % Polyline n 1026 582 m 1011 608 l gs col0 s gr % Polyline n 931 526 m 916 552 l gs col0 s gr % Polyline n 867 381 m 893 366 l gs col0 s gr % Polyline n 980 320 m 954 335 l gs col0 s gr [5.000000] 0 setdash % Polyline n 836 203 m 537 720 l clp gs col-1 s gr [] 0 setdash [5.000000] 0 setdash % Polyline n 1138 720 m 836 203 l clp gs col-1 s 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696.000 282.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 836.000 202.000 m 836.000 282.500 l 836.000 363.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 836.000 202.000 m 906.000 242.000 l 976.000 282.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 836.000 202.000 m 836.000 281.500 l 836.000 361.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 1057.000 581.000 m 1097.500 650.500 l 1138.000 720.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 977.000 720.000 m 1057.000 720.000 l 1137.000 720.000 l gs col0 s gr $F2psEnd %%EndDocument @endspecial 1888 3603 a @beginspecial 0 @llx 0 @lly 1062 @urx 683 @ury 1190 @rhi @setspecial %%BeginDocument: sqr1.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: /tmp/xfig-fig005759 %%Creator: fig2dev Version 2.1.8 Patchlevel 0 %%CreationDate: Wed Nov 6 15:29:11 1996 %%For: richard@sunelc2 (Christoph Richard, D8A08) %%Orientation: Portrait %%BoundingBox: 0 0 1062 683 %%Pages: 0 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /l {lineto} bind def /m {moveto} bind def /s {stroke} bind def /n {newpath} bind def /gs {gsave} bind def /gr {grestore} bind def /clp {closepath} bind def /graycol {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul setrgbcolor} bind def /col-1 {} def /col0 {0 0 0 setrgbcolor} bind def /col1 {0 0 1 setrgbcolor} bind def /col2 {0 1 0 setrgbcolor} bind def /col3 {0 1 1 setrgbcolor} bind def /col4 {1 0 0 setrgbcolor} bind def /col5 {1 0 1 setrgbcolor} bind def /col6 {1 1 0 setrgbcolor} bind def /col7 {1 1 1 setrgbcolor} bind def /col8 {.68 .85 .9 setrgbcolor} bind def /col9 {0 .39 0 setrgbcolor} bind def /col10 {.65 .17 .17 setrgbcolor} bind def /col11 {1 .51 0 setrgbcolor} bind def /col12 {.63 .13 .94 setrgbcolor} bind def /col13 {1 .75 .8 setrgbcolor} bind def /col14 {.7 .13 .13 setrgbcolor} bind def /col15 {1 .84 0 setrgbcolor} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y translate xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix } def /DrawSplineSection { /y3 exch def /x3 exch def /y2 exch def /x2 exch def /y1 exch def /x1 exch def /xa x1 x2 x1 sub 0.666667 mul add def /ya y1 y2 y1 sub 0.666667 mul add def /xb x3 x2 x3 sub 0.666667 mul add def /yb y3 y2 y3 sub 0.666667 mul add def x1 y1 lineto xa ya xb yb x3 y3 curveto } def end /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 0 setlinecap 0 setlinejoin -45.0 888.0 translate 0.900 -0.900 scale 0.500 setlinewidth % Ellipse n 754 659 7 7 0 360 DrawEllipse gs 0.00 setgray fill gr gs col0 s gr % Ellipse n 664 606 7 7 0 360 DrawEllipse gs 0.00 setgray fill gr gs col0 s gr % Rotated Ellipse gs 773 495 translate -150.000 rotate n 0 0 7 7 0 360 DrawEllipse gs 0.00 setgray fill gr gs col0 s gr gr % Rotated Ellipse gs 826 401 translate -150.000 rotate n 0 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159 550 l gs col0 s gr % Polyline n 742 527 m 727 501 l gs col0 s gr % Polyline n 187 660 m 157 660 l gs col0 s gr % Polyline n 68 660 m 98 660 l gs col0 s gr % Polyline n 80 535 m 80 565 l gs col0 s gr [5.000000] 0 setdash % Polyline n 552 309 m 551 907 l clp gs col-1 s gr [] 0 setdash [5.000000] 0 setdash % Polyline n 1148 307 m 552 308 l clp gs col-1 s gr [] 0 setdash [5.000000] 0 setdash % Polyline n 1149 906 m 1147 307 l 1148 307 l clp gs col-1 s gr [] 0 setdash [5.000000] 0 setdash % Polyline n 551 906 m 1149 906 l clp gs col-1 s gr [] 0 setdash % Open spline n 631.000 606.000 m 700.500 646.500 l 770.000 687.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 770.000 686.000 m 770.000 606.000 l 770.000 526.000 l gs col0 s gr % Open spline n 1068.000 606.000 m 1068.000 526.000 l 1068.000 446.000 l gs col0 s gr % Open spline n 930.000 687.000 m 999.500 646.500 l 1069.000 606.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 770.000 686.000 m 850.000 686.000 l 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DrawEllipse gs col0 s gr gr % Rotated Ellipse gs 1149 499 translate -90.012 rotate n 0 0 7 7 0 360 DrawEllipse gs col0 s gr gr % Rotated Ellipse gs 1204 589 translate -90.012 rotate n 0 0 7 7 0 360 DrawEllipse gs col0 s gr gr % Rotated Ellipse gs 1096 589 translate -90.012 rotate n 0 0 7 7 0 360 DrawEllipse gs col0 s gr gr % Rotated Ellipse gs 675 256 translate -180.023 rotate n 0 0 7 7 0 360 DrawEllipse gs 0.00 setgray fill gr gs col0 s gr gr % Rotated Ellipse gs 581 308 translate -180.023 rotate n 0 0 7 7 0 360 DrawEllipse gs 0.00 setgray fill gr gs col0 s gr gr % Rotated Ellipse gs 674 360 translate -180.023 rotate n 0 0 7 7 0 360 DrawEllipse gs 0.00 setgray fill gr gs col0 s gr gr % Rotated Ellipse gs 1028 256 translate -120.035 rotate n 0 0 7 7 0 360 DrawEllipse gs 0.00 setgray fill gr gs col0 s gr gr % Rotated Ellipse gs 569 438 translate -120.035 rotate n 0 0 7 7 0 360 DrawEllipse gs 0.00 setgray fill gr gs col0 s gr gr % Rotated Ellipse gs 504 782 translate -150.000 rotate n 0 0 7 7 0 360 DrawEllipse gs 0.00 setgray fill gr gs col0 s gr gr % Rotated Ellipse gs 902 512 translate -90.012 rotate n 0 0 7 7 0 360 DrawEllipse gs 0.00 setgray fill gr gs col0 s gr gr % Polyline n 770 526 m 770 686 l 930 686 l 930 526 l clp gs col0 s gr % Polyline n 771 525 m 690 386 l 553 465 l 633 605 l clp gs col0 s gr % Polyline n 631 766 m 712 905 l 850 825 l 770 686 l clp gs col0 s gr % Polyline n 850 825 m 988 905 l 1068 766 l 930 686 l clp gs col0 s gr % Polyline n 1068 605 m 1068 765 l 1228 765 l 1228 605 l clp gs col0 s gr % Polyline n 471 606 m 471 766 l 631 766 l 631 606 l clp gs col0 s gr % Polyline n 929 526 m 1069 606 l 1148 467 l 1010 387 l clp gs col0 s gr % Polyline n 691 228 m 691 388 l 851 388 l 851 228 l clp gs col0 s gr % Polyline n 851 228 m 851 388 l 1011 388 l 1011 228 l clp gs col0 s gr % Polyline n 259 604 m 389 604 l gs col-1 s gr n 359.000 589.000 m 389.000 604.000 l 359.000 619.000 l gs 2 setlinejoin col-1 s gr % Polyline n 48 526 m 48 686 l 208 686 l 208 526 l clp gs col0 s gr % Polyline n 179 541 m 179 571 l gs col0 s gr % Polyline n 72 540 m 72 570 l gs col0 s gr % Polyline n 837 251 m 807 251 l gs col0 s gr % Polyline n 836 358 m 806 358 l gs col0 s gr % Polyline n 866 251 m 896 251 l gs col0 s gr % Polyline n 865 359 m 895 359 l gs col0 s gr % Polyline n 986 373 m 986 343 l gs col0 s gr % Polyline n 986 239 m 986 269 l gs col0 s gr % Polyline n 690 416 m 664 431 l gs col0 s gr % Polyline n 575 482 m 601 467 l gs col0 s gr % Polyline n 634 579 m 660 564 l gs col0 s gr % Polyline n 741 528 m 726 502 l gs col0 s gr % Polyline n 785 550 m 815 550 l gs col0 s gr % Polyline n 919 551 m 889 551 l gs col0 s gr % Polyline n 906 673 m 906 643 l gs col0 s gr % Polyline n 797 674 m 797 644 l gs col0 s gr % Polyline n 959 526 m 974 500 l gs col0 s gr % Polyline n 1014 414 m 1040 429 l gs col0 s gr % Polyline n 1124 480 m 1098 465 l gs col0 s gr % Polyline n 1070 577 m 1044 562 l gs col0 s gr % Polyline n 1204 621 m 1204 651 l gs col0 s gr % Polyline n 1097 619 m 1097 649 l gs col0 s gr % Polyline n 1082 742 m 1112 742 l gs col0 s gr % Polyline n 1214 745 m 1184 745 l gs col0 s gr % Polyline n 499 619 m 499 649 l gs col0 s gr % Polyline n 606 623 m 606 653 l gs col0 s gr % Polyline n 621 738 m 591 738 l gs col0 s gr % Polyline n 490 738 m 520 738 l gs col0 s gr % Polyline n 767 713 m 741 728 l gs col0 s gr % Polyline n 821 809 m 795 824 l gs col0 s gr % Polyline n 727 881 m 712 855 l gs col0 s gr % Polyline n 664 766 m 679 792 l gs col0 s gr % Polyline n 973 882 m 988 856 l gs col0 s gr % Polyline n 878 810 m 904 825 l gs col0 s gr % Polyline n 932 716 m 958 731 l gs col0 s gr % Polyline n 192 656 m 162 656 l gs col0 s gr % Polyline n 63 656 m 93 656 l gs col0 s gr % Polyline n 724 374 m 724 344 l gs col0 s gr % Polyline n 724 240 m 724 270 l gs col0 s gr % Polyline n 1041 763 m 1026 789 l gs col0 s gr [5.000000] 0 setdash % Polyline n 553 307 m 1150 306 l 1150 305 l clp gs col-1 s gr [] 0 setdash 1 setlinecap [1 5.000000] 5.000000 setdash % Polyline n 552 308 m 550 907 l clp gs col-1 s gr [] 0 setdash 0 setlinecap [5.000000] 0 setdash % Polyline n 1150 307 m 1150 906 l clp gs col-1 s gr [] 0 setdash [5.000000] 0 setdash % Polyline n 551 907 m 1150 906 l clp gs col-1 s gr [] 0 setdash % Open spline n 631.000 606.000 m 700.500 646.500 l 770.000 687.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 770.000 686.000 m 770.000 606.000 l 770.000 526.000 l gs col0 s gr % Open spline n 930.000 687.000 m 999.500 646.500 l 1069.000 606.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 770.000 686.000 m 850.000 686.000 l 930.000 686.000 l gs col0 s gr % Open spline n 930.000 526.000 m 930.000 606.000 l 930.000 686.000 l gs col0 s gr % Open spline n 851.000 387.000 m 810.500 456.500 l 770.000 526.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 771.000 526.000 m 851.000 526.000 l 931.000 526.000 l gs col0 s gr % Open spline n 552.000 467.000 m 511.500 536.500 l 471.000 606.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 550.000 307.000 m 620.000 347.000 l 690.000 387.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 631.000 767.000 m 590.500 836.500 l 550.000 906.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 551.000 906.000 m 631.000 906.000 l 711.000 906.000 l gs col0 s gr % Open spline n 711.000 905.000 m 780.500 945.500 l 850.000 986.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 472.000 766.000 m 512.000 836.000 l 552.000 906.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 849.000 986.000 m 918.500 946.000 l 988.000 906.000 l gs col0 s gr % Open spline n 1069.000 767.000 m 1109.500 836.500 l 1150.000 906.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 989.000 906.000 m 1069.000 906.000 l 1149.000 906.000 l gs col0 s gr % Open spline n 1148.000 905.000 m 1188.500 835.000 l 1229.000 765.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 551.000 308.000 m 620.500 267.500 l 690.000 227.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 552.000 307.000 m 551.500 387.500 l 551.000 468.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 850.000 985.000 m 850.000 905.000 l 850.000 825.000 l gs col0 s gr % Open spline n 1012.000 227.000 m 1082.000 267.000 l 1152.000 307.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 1012.000 387.000 m 1081.500 347.000 l 1151.000 307.000 l gs col0 s gr % Open spline n 851.000 388.000 m 891.500 458.000 l 932.000 528.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 1149.000 466.000 m 1189.500 535.500 l 1230.000 605.000 l gs 0.00 setgray fill gr gs col0 s gr % Open spline n 1069.000 605.000 m 1149.000 605.000 l 1229.000 605.000 l gs col0 s gr % Open spline n 1150.000 466.000 m 1150.000 385.500 l 1150.000 305.000 l gs col0 s gr $F2psEnd %%EndDocument @endspecial 456 4869 a(Figure)h(2:)43 b(In\015ation)32 b(rules)g(for)g(the)h(square-triangle)f(tiling)d(class)k(LI[ST].)1817 5471 y(18)p eop %%Page: 19 19 19 18 bop 331 3378 a @beginspecial 150 @llx 60 @lly 570 @urx 480 @ury 3685 @rhi @setspecial %%BeginDocument: stpatch.eps %!PS-Adobe-3.0 EPSF %%Title: Maple plot %%Creator: MapleV %%Pages: 1 %%BoundingBox: 150 60 570 480 %%DocumentNeededResources: font Courier %%EndComments 20 dict begin gsave /m {moveto} def /l {lineto} def /C {setrgbcolor} def /G {setgray} def /S {stroke} def /NP {newpath} def %%%%This draws a filled polygon and avoids bugs/features %%%% of some postscript interpreters %%%%GHOSTSCRIPT: has a bug in reversepath - removing %%%%the call to reversepath is a sufficient work around /P {gsave fill grestore reversepath stroke} def %%%%This function is needed for drawing text /stringbbox {gsave NP 0 0 m false charpath flattenpath pathbbox 4 2 roll pop pop 1.1 mul cvi exch 1.1 mul cvi exch grestore} def /thin 3 def /medium 5 def /thick 7 def /boundarythick 20 def %% thickness of bounding box %%IncludeResource: font Courier %%576 36 translate %%90 rotate 0.108 0.108 scale 1 setlinejoin 1 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m 2886 4164 l 2955 4044 l 3024 4164 l S NP 2886 4164 m 2817 4044 l 2955 4044 l 2886 4164 l S NP 3074 3837 m 3212 3837 l 3212 3975 l 3074 3975 l 3074 3837 l S NP 3212 3837 m 3074 3837 l 3143 3717 l 3212 3837 l S NP 3143 3717 m 3074 3837 l 3005 3717 l 3143 3717 l S NP 3074 3598 m 3143 3717 l 3005 3717 l 3074 3598 l S NP 2886 3648 m 2955 3529 l 3074 3598 l 3005 3717 l 2886 3648 l S NP 3212 3975 m 3143 4095 l 3074 3975 l 3212 3975 l S NP 2955 3906 m 2955 4044 l 2817 4044 l 2817 3906 l 2955 3906 l 2817 3906 l 2886 3786 l 2955 3906 l S NP 2817 3906 m 2697 3837 l 2766 3717 l 2886 3786 l 2817 3906 l S NP 2628 3717 m 2766 3717 l 2697 3837 l 2628 3717 l S NP 2955 3529 m 2886 3648 l 2817 3529 l 2955 3529 l S NP 3074 3837 m 3074 3975 l 2955 3906 l 3074 3837 l S NP 3005 3717 m 2886 3786 l 2886 3648 l 3005 3717 l S NP 2886 3786 m 3005 3717 l 3074 3837 l 2955 3906 l 2886 3786 l S NP 3143 4095 m 3024 4164 l 2955 4044 l 3074 3975 l 3143 4095 l S NP 2955 4044 m 2955 3906 l 3074 3975 l 2955 4044 l S NP 2628 3717 m 2697 3598 l 2766 3717 l 2628 3717 l S NP 2817 4044 m 2697 3975 l 2817 3906 l 2817 4044 l S NP 2697 3837 m 2817 3906 l 2697 3975 l 2697 3837 l S NP 3778 4164 m 3709 4283 l 3640 4164 l 3778 4164 l 3640 4164 l 3709 4044 l 3778 4164 l S NP 3520 4233 m 3640 4164 l 3709 4283 l 3589 4352 l 3520 4233 l S NP 3589 3975 m 3709 4044 l 3640 4164 l 3520 4095 l 3589 3975 l S NP 3640 4164 m 3520 4233 l 3520 4095 l 3640 4164 l S NP 3589 4352 m 3451 4352 l 3520 4233 l 3589 4352 l S NP 3589 3975 m 3520 4095 l 3451 3975 l 3589 3975 l S NP 3401 4164 m 3520 4095 l 3520 4233 l 3401 4164 l S NP 3451 4352 m 3332 4421 l 3332 4283 l 3451 4352 l S NP 3451 3975 m 3332 4044 l 3332 3906 l 3451 3975 l S NP 3332 4283 m 3263 4164 l 3401 4164 l 3332 4283 l S NP 3332 4044 m 3401 4164 l 3263 4164 l 3332 4044 l S NP 3520 4233 m 3451 4352 l 3332 4283 l 3401 4164 l 3520 4233 l S NP 3401 4164 m 3332 4044 l 3451 3975 l 3520 4095 l 3401 4164 l S NP 2886 4164 m 2955 4044 l 3024 4164 l 2886 4164 l 3024 4164 l 2955 4283 l 2886 4164 l S NP 3143 4095 m 3024 4164 l 2955 4044 l 3074 3975 l 3143 4095 l S NP 3074 4352 m 2955 4283 l 3024 4164 l 3143 4233 l 3074 4352 l S NP 3024 4164 m 3143 4095 l 3143 4233 l 3024 4164 l S NP 3074 3975 m 3212 3975 l 3143 4095 l 3074 3975 l S NP 3074 4352 m 3143 4233 l 3212 4352 l 3074 4352 l S NP 3263 4164 m 3143 4233 l 3143 4095 l 3263 4164 l S NP 3212 3975 m 3332 3906 l 3332 4044 l 3212 3975 l S NP 3212 4352 m 3332 4283 l 3332 4421 l 3212 4352 l S NP 3332 4044 m 3401 4164 l 3263 4164 l 3332 4044 l S NP 3332 4283 m 3263 4164 l 3401 4164 l 3332 4283 l S NP 3143 4095 m 3212 3975 l 3332 4044 l 3263 4164 l 3143 4095 l S NP 3263 4164 m 3332 4283 l 3212 4352 l 3143 4233 l 3263 4164 l S NP 3332 2499 m 3263 2618 l 3194 2499 l 3332 2499 l S NP 3074 2568 m 3194 2499 l 3263 2618 l 3143 2687 l 3074 2568 l S NP 3194 2499 m 3074 2568 l 3074 2430 l 3194 2499 l S NP 3263 2618 m 3263 2756 l 3143 2687 l 3263 2618 l S NP 3143 2825 m 3143 2687 l 3263 2756 l 3143 2825 l S NP 2955 2499 m 3074 2430 l 3074 2568 l 2955 2499 l S NP 3143 2825 m 3074 2945 l 3005 2825 l 3143 2825 l S NP 2955 2499 m 2886 2618 l 2817 2499 l 2955 2499 l S NP 3005 2687 m 3074 2568 l 3143 2687 l 3005 2687 l S NP 3143 2687 m 3143 2825 l 3005 2825 l 3005 2687 l 3143 2687 l S NP 3005 2687 m 2886 2618 l 2955 2499 l 3074 2568 l 3005 2687 l S NP 3005 2825 m 2886 2756 l 3005 2687 l 3005 2825 l S NP 2886 2618 m 3005 2687 l 2886 2756 l 2886 2618 l S NP 2371 2756 m 2490 2825 l 2371 2894 l 2371 2756 l S NP 2440 3014 m 2371 2894 l 2490 2825 l 2559 2945 l 2440 3014 l S NP 2559 2945 m 2628 3064 l 2509 3133 l 2440 3014 l 2559 2945 l S NP 2628 3202 m 2509 3133 l 2628 3064 l 2628 3202 l S NP 2371 2756 m 2490 2687 l 2490 2825 l 2371 2756 l S NP 2628 3202 m 2628 3064 l 2748 3133 l 2628 3202 l S NP 2936 2945 m 2817 3014 l 2817 2876 l 2936 2945 l S NP 2817 3014 m 2936 2945 l 3005 3064 l 2886 3133 l 2817 3014 l S NP 2679 2499 m 2817 2499 l 2748 2618 l 2679 2499 l S NP 2817 2499 m 2886 2618 l 2748 2618 l 2817 2499 l S NP 2628 2825 m 2490 2825 l 2490 2687 l 2628 2687 l 2628 2825 l S NP 2490 2825 m 2628 2825 l 2559 2945 l 2490 2825 l S NP 2559 2945 m 2628 2825 l 2697 2945 l 2559 2945 l S NP 2628 3064 m 2559 2945 l 2697 2945 l 2628 3064 l S NP 2817 3014 m 2748 3133 l 2628 3064 l 2697 2945 l 2817 3014 l S NP 2490 2687 m 2559 2568 l 2628 2687 l 2490 2687 l S NP 2748 2756 m 2748 2618 l 2886 2618 l 2886 2756 l 2748 2756 l 2886 2756 l 2817 2876 l 2748 2756 l S NP 2886 2756 m 3005 2825 l 2936 2945 l 2817 2876 l 2886 2756 l S NP 3074 2945 m 2936 2945 l 3005 2825 l 3074 2945 l S NP 2748 3133 m 2817 3014 l 2886 3133 l 2748 3133 l S NP 2628 2825 m 2628 2687 l 2748 2756 l 2628 2825 l S NP 2697 2945 m 2817 2876 l 2817 3014 l 2697 2945 l S NP 2817 2876 m 2697 2945 l 2628 2825 l 2748 2756 l 2817 2876 l S NP 2559 2568 m 2679 2499 l 2748 2618 l 2628 2687 l 2559 2568 l S NP 2748 2618 m 2748 2756 l 2628 2687 l 2748 2618 l S NP 3074 2945 m 3005 3064 l 2936 2945 l 3074 2945 l S NP 2886 2618 m 3005 2687 l 2886 2756 l 2886 2618 l S NP 3005 2825 m 2886 2756 l 3005 2687 l 3005 2825 l S NP 2817 2499 m 2748 2618 l 2679 2499 l 2817 2499 l 2679 2499 l 2748 2379 l 2817 2499 l S NP 2559 2568 m 2679 2499 l 2748 2618 l 2628 2687 l 2559 2568 l S NP 2628 2310 m 2748 2379 l 2679 2499 l 2559 2430 l 2628 2310 l S NP 2679 2499 m 2559 2568 l 2559 2430 l 2679 2499 l S NP 2628 2687 m 2490 2687 l 2559 2568 l 2628 2687 l S NP 2628 2310 m 2559 2430 l 2490 2310 l 2628 2310 l S NP 2440 2499 m 2559 2430 l 2559 2568 l 2440 2499 l S NP 2490 2687 m 2371 2756 l 2371 2618 l 2490 2687 l S NP 2490 2310 m 2371 2379 l 2371 2241 l 2490 2310 l S NP 2371 2618 m 2302 2499 l 2440 2499 l 2371 2618 l S NP 2371 2379 m 2440 2499 l 2302 2499 l 2371 2379 l S NP 2559 2568 m 2490 2687 l 2371 2618 l 2440 2499 l 2559 2568 l S NP 2440 2499 m 2371 2379 l 2490 2310 l 2559 2430 l 2440 2499 l S NP 3074 2945 m 3143 3064 l 3005 3064 l 3074 2945 l 3005 3064 l 2936 2945 l 3074 2945 l S NP 3005 3202 m 3005 3064 l 3143 3064 l 3143 3202 l 3005 3202 l S NP 2817 3014 m 2936 2945 l 3005 3064 l 2886 3133 l 2817 3014 l S NP 3005 3064 m 3005 3202 l 2886 3133 l 3005 3064 l S NP 3143 3202 m 3074 3322 l 3005 3202 l 3143 3202 l S NP 2817 3014 m 2886 3133 l 2748 3133 l 2817 3014 l S NP 2886 3271 m 2886 3133 l 3005 3202 l 2886 3271 l S NP 3074 3322 m 3074 3460 l 2955 3391 l 3074 3322 l S NP 2748 3133 m 2748 3271 l 2628 3202 l 2748 3133 l S NP 2955 3391 m 2817 3391 l 2886 3271 l 2955 3391 l S NP 2748 3271 m 2886 3271 l 2817 3391 l 2748 3271 l S NP 3005 3202 m 3074 3322 l 2955 3391 l 2886 3271 l 3005 3202 l S NP 2886 3271 m 2748 3271 l 2748 3133 l 2886 3133 l 2886 3271 l S NP 2628 3717 m 2559 3598 l 2697 3598 l 2628 3717 l 2697 3598 l 2766 3717 l 2628 3717 l S NP 2697 3460 m 2697 3598 l 2559 3598 l 2559 3460 l 2697 3460 l S NP 2886 3648 m 2766 3717 l 2697 3598 l 2817 3529 l 2886 3648 l S NP 2697 3598 m 2697 3460 l 2817 3529 l 2697 3598 l S NP 2559 3460 m 2628 3340 l 2697 3460 l 2559 3460 l S NP 2886 3648 m 2817 3529 l 2955 3529 l 2886 3648 l S NP 2817 3391 m 2817 3529 l 2697 3460 l 2817 3391 l S NP 2628 3340 m 2628 3202 l 2748 3271 l 2628 3340 l S NP 2955 3529 m 2955 3391 l 3074 3460 l 2955 3529 l S NP 2748 3271 m 2886 3271 l 2817 3391 l 2748 3271 l S NP 2955 3391 m 2817 3391 l 2886 3271 l 2955 3391 l S NP 2697 3460 m 2628 3340 l 2748 3271 l 2817 3391 l 2697 3460 l S NP 2817 3391 m 2955 3391 l 2955 3529 l 2817 3529 l 2817 3391 l S NP 1924 2499 m 1993 2379 l 2062 2499 l 1924 2499 l 2062 2499 l 1993 2618 l 1924 2499 l S NP 2182 2430 m 2062 2499 l 1993 2379 l 2113 2310 l 2182 2430 l S NP 2113 2687 m 1993 2618 l 2062 2499 l 2182 2568 l 2113 2687 l S NP 2062 2499 m 2182 2430 l 2182 2568 l 2062 2499 l S NP 2113 2310 m 2251 2310 l 2182 2430 l 2113 2310 l S NP 2113 2687 m 2182 2568 l 2251 2687 l 2113 2687 l S NP 2302 2499 m 2182 2568 l 2182 2430 l 2302 2499 l S NP 2251 2310 m 2371 2241 l 2371 2379 l 2251 2310 l S NP 2251 2687 m 2371 2618 l 2371 2756 l 2251 2687 l S NP 2371 2379 m 2440 2499 l 2302 2499 l 2371 2379 l S NP 2371 2618 m 2302 2499 l 2440 2499 l 2371 2618 l S NP 2182 2430 m 2251 2310 l 2371 2379 l 2302 2499 l 2182 2430 l S NP 2302 2499 m 2371 2618 l 2251 2687 l 2182 2568 l 2302 2499 l S NP 2628 3717 m 2559 3837 l 2490 3717 l 2628 3717 l S NP 2371 3786 m 2490 3717 l 2559 3837 l 2440 3906 l 2371 3786 l S NP 2490 3717 m 2371 3786 l 2371 3648 l 2490 3717 l S NP 2559 3837 m 2559 3975 l 2440 3906 l 2559 3837 l S NP 2440 4044 m 2440 3906 l 2559 3975 l 2440 4044 l S NP 2251 3717 m 2371 3648 l 2371 3786 l 2251 3717 l S NP 2440 4044 m 2371 4164 l 2302 4044 l 2440 4044 l S NP 2251 3717 m 2182 3837 l 2113 3717 l 2251 3717 l S NP 2302 3906 m 2371 3786 l 2440 3906 l 2302 3906 l S NP 2440 3906 m 2440 4044 l 2302 4044 l 2302 3906 l 2440 3906 l S NP 2302 3906 m 2182 3837 l 2251 3717 l 2371 3786 l 2302 3906 l S NP 2302 4044 m 2182 3975 l 2302 3906 l 2302 4044 l S NP 2182 3837 m 2302 3906 l 2182 3975 l 2182 3837 l S NP 1924 2499 m 1855 2618 l 1786 2499 l 1924 2499 l S NP 1667 2568 m 1786 2499 l 1855 2618 l 1736 2687 l 1667 2568 l S NP 1786 2499 m 1667 2568 l 1667 2430 l 1786 2499 l S NP 1855 2618 m 1855 2756 l 1736 2687 l 1855 2618 l S NP 1736 2825 m 1736 2687 l 1855 2756 l 1736 2825 l S NP 1547 2499 m 1667 2430 l 1667 2568 l 1547 2499 l S NP 1736 2825 m 1667 2945 l 1598 2825 l 1736 2825 l S NP 1547 2499 m 1478 2618 l 1409 2499 l 1547 2499 l S NP 1598 2687 m 1667 2568 l 1736 2687 l 1598 2687 l S NP 1736 2687 m 1736 2825 l 1598 2825 l 1598 2687 l 1736 2687 l S NP 1598 2687 m 1478 2618 l 1547 2499 l 1667 2568 l 1598 2687 l S NP 1598 2825 m 1478 2756 l 1598 2687 l 1598 2825 l S NP 1478 2618 m 1598 2687 l 1478 2756 l 1478 2618 l S NP 2113 3202 m 2113 3064 l 2233 3133 l 2113 3202 l 2233 3133 l 2233 3271 l 2113 3202 l S NP 2302 3014 m 2233 3133 l 2113 3064 l 2182 2945 l 2302 3014 l S NP 2371 3271 m 2233 3271 l 2233 3133 l 2371 3133 l 2371 3271 l S NP 2233 3133 m 2302 3014 l 2371 3133 l 2233 3133 l S NP 2182 2945 m 2251 2825 l 2371 2894 l 2302 3014 l 2182 2945 l S NP 2371 3133 m 2509 3133 l 2509 3271 l 2371 3271 l 2371 3133 l S NP 2371 2894 m 2440 3014 l 2302 3014 l 2371 2894 l S NP 2509 3133 m 2371 3133 l 2440 3014 l 2509 3133 l S NP 2302 3014 m 2440 3014 l 2371 3133 l 2302 3014 l S NP 2371 2756 m 2490 2825 l 2371 2894 l 2371 2756 l S NP 2628 3202 m 2509 3133 l 2628 3064 l 2628 3202 l S NP 2440 3014 m 2371 2894 l 2490 2825 l 2559 2945 l 2440 3014 l S NP 2559 2945 m 2628 3064 l 2509 3133 l 2440 3014 l 2559 2945 l S NP 2371 2756 m 2371 2894 l 2251 2825 l 2371 2756 l S NP 2628 3202 m 2509 3271 l 2509 3133 l 2628 3202 l 2509 3271 l 2509 3133 l 2628 3202 l S NP 2371 3133 m 2509 3133 l 2509 3271 l 2371 3271 l 2371 3133 l S NP 2371 3271 m 2233 3271 l 2233 3133 l 2371 3133 l 2371 3271 l S NP 2113 3202 m 2233 3133 l 2233 3271 l 2113 3202 l S NP 2628 3202 m 2628 3340 l 2509 3271 l 2628 3202 l S NP 2113 3202 m 2233 3271 l 2113 3340 l 2113 3202 l S NP 2182 3598 m 2182 3460 l 2302 3529 l 2182 3598 l S NP 2182 3460 m 2182 3598 l 2044 3598 l 2044 3460 l 2182 3460 l S NP 2697 3598 m 2628 3717 l 2559 3598 l 2697 3598 l S NP 2628 3717 m 2490 3717 l 2559 3598 l 2628 3717 l S NP 2440 3391 m 2509 3271 l 2628 3340 l 2559 3460 l 2440 3391 l S NP 2509 3271 m 2440 3391 l 2371 3271 l 2509 3271 l S NP 2371 3271 m 2440 3391 l 2302 3391 l 2371 3271 l S NP 2233 3271 m 2371 3271 l 2302 3391 l 2233 3271 l S NP 2182 3460 m 2113 3340 l 2233 3271 l 2302 3391 l 2182 3460 l S NP 2628 3340 m 2697 3460 l 2559 3460 l 2628 3340 l S NP 2440 3529 m 2559 3598 l 2490 3717 l 2371 3648 l 2440 3529 l 2371 3648 l 2302 3529 l 2440 3529 l S NP 2371 3648 m 2251 3717 l 2182 3598 l 2302 3529 l 2371 3648 l S NP 2113 3717 m 2182 3598 l 2251 3717 l 2113 3717 l S NP 2113 3340 m 2182 3460 l 2044 3460 l 2113 3340 l S NP 2440 3391 m 2559 3460 l 2440 3529 l 2440 3391 l S NP 2302 3391 m 2302 3529 l 2182 3460 l 2302 3391 l S NP 2302 3529 m 2302 3391 l 2440 3391 l 2440 3529 l 2302 3529 l S NP 2697 3460 m 2697 3598 l 2559 3598 l 2559 3460 l 2697 3460 l S NP 2559 3598 m 2440 3529 l 2559 3460 l 2559 3598 l S NP 2113 3717 m 2044 3598 l 2182 3598 l 2113 3717 l S NP 2490 3717 m 2371 3786 l 2371 3648 l 2490 3717 l S NP 2251 3717 m 2371 3648 l 2371 3786 l 2251 3717 l S NP 2113 3202 m 2113 3064 l 2233 3133 l 2113 3202 l S NP 2302 3014 m 2233 3133 l 2113 3064 l 2182 2945 l 2302 3014 l S NP 2182 2945 m 2251 2825 l 2371 2894 l 2302 3014 l 2182 2945 l S NP 2371 2756 m 2371 2894 l 2251 2825 l 2371 2756 l S NP 2113 3202 m 1993 3133 l 2113 3064 l 2113 3202 l S NP 2371 2756 m 2251 2825 l 2251 2687 l 2371 2756 l S NP 1993 2618 m 2113 2687 l 1993 2756 l 1993 2618 l S NP 2113 2687 m 1993 2618 l 2062 2499 l 2182 2568 l 2113 2687 l S NP 1736 3064 m 1667 2945 l 1805 2945 l 1736 3064 l S NP 1667 2945 m 1736 2825 l 1805 2945 l 1667 2945 l S NP 2044 2945 m 2113 3064 l 1993 3133 l 1924 3014 l 2044 2945 l S NP 2113 3064 m 2044 2945 l 2182 2945 l 2113 3064 l S NP 2182 2945 m 2044 2945 l 2113 2825 l 2182 2945 l S NP 2251 2825 m 2182 2945 l 2113 2825 l 2251 2825 l S NP 2113 2687 m 2251 2687 l 2251 2825 l 2113 2825 l 2113 2687 l S NP 1993 3133 m 1855 3133 l 1924 3014 l 1993 3133 l S NP 1924 2876 m 1805 2945 l 1736 2825 l 1855 2756 l 1924 2876 l 1855 2756 l 1993 2756 l 1924 2876 l S NP 1855 2756 m 1855 2618 l 1993 2618 l 1993 2756 l 1855 2756 l S NP 1924 2499 m 1993 2618 l 1855 2618 l 1924 2499 l S NP 2251 2687 m 2113 2687 l 2182 2568 l 2251 2687 l S NP 2044 2945 m 1924 3014 l 1924 2876 l 2044 2945 l S NP 2113 2825 m 1993 2756 l 2113 2687 l 2113 2825 l S NP 1993 2756 m 2113 2825 l 2044 2945 l 1924 2876 l 1993 2756 l S NP 1855 3133 m 1736 3064 l 1805 2945 l 1924 3014 l 1855 3133 l S NP 1805 2945 m 1924 2876 l 1924 3014 l 1805 2945 l S NP 1924 2499 m 2062 2499 l 1993 2618 l 1924 2499 l S NP 1736 2825 m 1736 2687 l 1855 2756 l 1736 2825 l S NP 1855 2618 m 1855 2756 l 1736 2687 l 1855 2618 l S NP 2113 3717 m 1975 3717 l 2044 3598 l 2113 3717 l 2044 3598 l 2182 3598 l 2113 3717 l S NP 1924 3529 m 2044 3598 l 1975 3717 l 1855 3648 l 1924 3529 l S NP 2182 3460 m 2182 3598 l 2044 3598 l 2044 3460 l 2182 3460 l S NP 2044 3598 m 1924 3529 l 2044 3460 l 2044 3598 l S NP 1855 3648 m 1786 3529 l 1924 3529 l 1855 3648 l S NP 2182 3460 m 2044 3460 l 2113 3340 l 2182 3460 l S NP 1924 3391 m 2044 3460 l 1924 3529 l 1924 3391 l S NP 1786 3529 m 1667 3460 l 1786 3391 l 1786 3529 l S NP 2113 3340 m 1993 3271 l 2113 3202 l 2113 3340 l S NP 1786 3391 m 1855 3271 l 1924 3391 l 1786 3391 l S NP 1993 3271 m 1924 3391 l 1855 3271 l 1993 3271 l S NP 1924 3529 m 1786 3529 l 1786 3391 l 1924 3391 l 1924 3529 l S NP 1924 3391 m 1993 3271 l 2113 3340 l 2044 3460 l 1924 3391 l S NP 1667 2945 m 1805 2945 l 1736 3064 l 1667 2945 l 1736 3064 l 1598 3064 l 1667 2945 l S NP 1855 3133 m 1736 3064 l 1805 2945 l 1924 3014 l 1855 3133 l S NP 1598 3202 m 1598 3064 l 1736 3064 l 1736 3202 l 1598 3202 l S NP 1736 3064 m 1855 3133 l 1736 3202 l 1736 3064 l S NP 1924 3014 m 1993 3133 l 1855 3133 l 1924 3014 l S NP 1598 3202 m 1736 3202 l 1667 3322 l 1598 3202 l S NP 1855 3271 m 1736 3202 l 1855 3133 l 1855 3271 l S NP 1993 3133 m 2113 3202 l 1993 3271 l 1993 3133 l S NP 1667 3322 m 1786 3391 l 1667 3460 l 1667 3322 l S NP 1993 3271 m 1924 3391 l 1855 3271 l 1993 3271 l S NP 1786 3391 m 1855 3271 l 1924 3391 l 1786 3391 l S NP 1855 3133 m 1993 3133 l 1993 3271 l 1855 3271 l 1855 3133 l S NP 1855 3271 m 1786 3391 l 1667 3322 l 1736 3202 l 1855 3271 l S NP 3332 2499 m 3194 2499 l 3263 2379 l 3332 2499 l S NP 3143 2310 m 3263 2379 l 3194 2499 l 3074 2430 l 3143 2310 l S NP 3263 2379 m 3143 2310 l 3263 2241 l 3263 2379 l S NP 3194 2499 m 3074 2568 l 3074 2430 l 3194 2499 l S NP 2955 2499 m 3074 2430 l 3074 2568 l 2955 2499 l S NP 3143 2172 m 3263 2241 l 3143 2310 l 3143 2172 l S NP 2955 2499 m 2817 2499 l 2886 2379 l 2955 2499 l S NP 3143 2172 m 3005 2172 l 3074 2053 l 3143 2172 l S NP 3005 2310 m 3143 2310 l 3074 2430 l 3005 2310 l S NP 3074 2430 m 2955 2499 l 2886 2379 l 3005 2310 l 3074 2430 l S NP 3005 2310 m 3005 2172 l 3143 2172 l 3143 2310 l 3005 2310 l S NP 2886 2379 m 2886 2241 l 3005 2310 l 2886 2379 l S NP 3005 2172 m 3005 2310 l 2886 2241 l 3005 2172 l S NP 2628 1795 m 2628 1933 l 2509 1864 l 2628 1795 l S NP 2440 1984 m 2509 1864 l 2628 1933 l 2559 2053 l 2440 1984 l S NP 2559 2053 m 2490 2172 l 2371 2103 l 2440 1984 l 2559 2053 l S NP 2371 2241 m 2371 2103 l 2490 2172 l 2371 2241 l S NP 2628 1795 m 2748 1864 l 2628 1933 l 2628 1795 l S NP 2371 2241 m 2490 2172 l 2490 2310 l 2371 2241 l S NP 2748 2379 m 2628 2310 l 2748 2241 l 2748 2379 l S NP 2628 2310 m 2748 2379 l 2679 2499 l 2559 2430 l 2628 2310 l S NP 3005 1933 m 3074 2053 l 2936 2053 l 3005 1933 l S NP 3074 2053 m 3005 2172 l 2936 2053 l 3074 2053 l S NP 2697 2053 m 2628 1933 l 2748 1864 l 2817 1984 l 2697 2053 l S NP 2628 1933 m 2697 2053 l 2559 2053 l 2628 1933 l S NP 2559 2053 m 2697 2053 l 2628 2172 l 2559 2053 l S NP 2490 2172 m 2559 2053 l 2628 2172 l 2490 2172 l S NP 2628 2310 m 2490 2310 l 2490 2172 l 2628 2172 l 2628 2310 l S NP 2748 1864 m 2886 1864 l 2817 1984 l 2748 1864 l S NP 2817 2122 m 2936 2053 l 3005 2172 l 2886 2241 l 2817 2122 l 2886 2241 l 2748 2241 l 2817 2122 l S NP 2886 2241 m 2886 2379 l 2748 2379 l 2748 2241 l 2886 2241 l S NP 2817 2499 m 2748 2379 l 2886 2379 l 2817 2499 l S NP 2490 2310 m 2628 2310 l 2559 2430 l 2490 2310 l S NP 2697 2053 m 2817 1984 l 2817 2122 l 2697 2053 l S NP 2628 2172 m 2748 2241 l 2628 2310 l 2628 2172 l S NP 2748 2241 m 2628 2172 l 2697 2053 l 2817 2122 l 2748 2241 l S NP 2886 1864 m 3005 1933 l 2936 2053 l 2817 1984 l 2886 1864 l S NP 2936 2053 m 2817 2122 l 2817 1984 l 2936 2053 l S NP 2817 2499 m 2679 2499 l 2748 2379 l 2817 2499 l S NP 3005 2172 m 3005 2310 l 2886 2241 l 3005 2172 l S NP 2886 2379 m 2886 2241 l 3005 2310 l 2886 2379 l S NP 3074 2053 m 2936 2053 l 3005 1933 l 3074 2053 l 3005 1933 l 3143 1933 l 3074 2053 l S NP 2886 1864 m 3005 1933 l 2936 2053 l 2817 1984 l 2886 1864 l S NP 3143 1795 m 3143 1933 l 3005 1933 l 3005 1795 l 3143 1795 l S NP 3005 1933 m 2886 1864 l 3005 1795 l 3005 1933 l S NP 2817 1984 m 2748 1864 l 2886 1864 l 2817 1984 l S NP 3143 1795 m 3005 1795 l 3074 1676 l 3143 1795 l S NP 2886 1726 m 3005 1795 l 2886 1864 l 2886 1726 l S NP 2748 1864 m 2628 1795 l 2748 1726 l 2748 1864 l S NP 3074 1676 m 2955 1607 l 3074 1538 l 3074 1676 l S NP 2748 1726 m 2817 1607 l 2886 1726 l 2748 1726 l S NP 2955 1607 m 2886 1726 l 2817 1607 l 2955 1607 l S NP 2886 1864 m 2748 1864 l 2748 1726 l 2886 1726 l 2886 1864 l S NP 2886 1726 m 2955 1607 l 3074 1676 l 3005 1795 l 2886 1726 l S NP 2817 2499 m 2748 2618 l 2679 2499 l 2817 2499 l 2679 2499 l 2748 2379 l 2817 2499 l S NP 2559 2568 m 2679 2499 l 2748 2618 l 2628 2687 l 2559 2568 l S NP 2628 2310 m 2748 2379 l 2679 2499 l 2559 2430 l 2628 2310 l S NP 2679 2499 m 2559 2568 l 2559 2430 l 2679 2499 l S NP 2628 2687 m 2490 2687 l 2559 2568 l 2628 2687 l S NP 2628 2310 m 2559 2430 l 2490 2310 l 2628 2310 l S NP 2440 2499 m 2559 2430 l 2559 2568 l 2440 2499 l S NP 2490 2687 m 2371 2756 l 2371 2618 l 2490 2687 l S NP 2490 2310 m 2371 2379 l 2371 2241 l 2490 2310 l S NP 2371 2618 m 2302 2499 l 2440 2499 l 2371 2618 l S NP 2371 2379 m 2440 2499 l 2302 2499 l 2371 2379 l S NP 2559 2568 m 2490 2687 l 2371 2618 l 2440 2499 l 2559 2568 l S NP 2440 2499 m 2371 2379 l 2490 2310 l 2559 2430 l 2440 2499 l S NP 1924 2499 m 1993 2379 l 2062 2499 l 1924 2499 l 2062 2499 l 1993 2618 l 1924 2499 l S NP 2182 2430 m 2062 2499 l 1993 2379 l 2113 2310 l 2182 2430 l S NP 2113 2687 m 1993 2618 l 2062 2499 l 2182 2568 l 2113 2687 l S NP 2062 2499 m 2182 2430 l 2182 2568 l 2062 2499 l S NP 2113 2310 m 2251 2310 l 2182 2430 l 2113 2310 l S NP 2113 2687 m 2182 2568 l 2251 2687 l 2113 2687 l S NP 2302 2499 m 2182 2568 l 2182 2430 l 2302 2499 l S NP 2251 2310 m 2371 2241 l 2371 2379 l 2251 2310 l S NP 2251 2687 m 2371 2618 l 2371 2756 l 2251 2687 l S NP 2371 2379 m 2440 2499 l 2302 2499 l 2371 2379 l S NP 2371 2618 m 2302 2499 l 2440 2499 l 2371 2618 l S NP 2182 2430 m 2251 2310 l 2371 2379 l 2302 2499 l 2182 2430 l S NP 2302 2499 m 2371 2618 l 2251 2687 l 2182 2568 l 2302 2499 l S NP 2628 1280 m 2766 1280 l 2697 1400 l 2628 1280 l 2697 1400 l 2559 1400 l 2628 1280 l S NP 2817 1469 m 2697 1400 l 2766 1280 l 2886 1349 l 2817 1469 l S NP 2559 1538 m 2559 1400 l 2697 1400 l 2697 1538 l 2559 1538 l S NP 2697 1400 m 2817 1469 l 2697 1538 l 2697 1400 l S NP 2886 1349 m 2955 1469 l 2817 1469 l 2886 1349 l S NP 2559 1538 m 2697 1538 l 2628 1657 l 2559 1538 l S NP 2817 1607 m 2697 1538 l 2817 1469 l 2817 1607 l S NP 2955 1469 m 3074 1538 l 2955 1607 l 2955 1469 l S NP 2628 1657 m 2748 1726 l 2628 1795 l 2628 1657 l S NP 2955 1607 m 2886 1726 l 2817 1607 l 2955 1607 l S NP 2748 1726 m 2817 1607 l 2886 1726 l 2748 1726 l S NP 2817 1469 m 2955 1469 l 2955 1607 l 2817 1607 l 2817 1469 l S NP 2817 1607 m 2748 1726 l 2628 1657 l 2697 1538 l 2817 1607 l S NP 1924 2499 m 1786 2499 l 1855 2379 l 1924 2499 l S NP 1736 2310 m 1855 2379 l 1786 2499 l 1667 2430 l 1736 2310 l S NP 1855 2379 m 1736 2310 l 1855 2241 l 1855 2379 l S NP 1786 2499 m 1667 2568 l 1667 2430 l 1786 2499 l S NP 1547 2499 m 1667 2430 l 1667 2568 l 1547 2499 l S NP 1736 2172 m 1855 2241 l 1736 2310 l 1736 2172 l S NP 1547 2499 m 1409 2499 l 1478 2379 l 1547 2499 l S NP 1736 2172 m 1598 2172 l 1667 2053 l 1736 2172 l S NP 1598 2310 m 1736 2310 l 1667 2430 l 1598 2310 l S NP 1667 2430 m 1547 2499 l 1478 2379 l 1598 2310 l 1667 2430 l S NP 1598 2310 m 1598 2172 l 1736 2172 l 1736 2310 l 1598 2310 l S NP 1478 2379 m 1478 2241 l 1598 2310 l 1478 2379 l S NP 1598 2172 m 1598 2310 l 1478 2241 l 1598 2172 l S NP 2628 1280 m 2490 1280 l 2559 1160 l 2628 1280 l S NP 2440 1091 m 2559 1160 l 2490 1280 l 2371 1211 l 2440 1091 l S NP 2559 1160 m 2440 1091 l 2559 1022 l 2559 1160 l S NP 2490 1280 m 2371 1349 l 2371 1211 l 2490 1280 l S NP 2251 1280 m 2371 1211 l 2371 1349 l 2251 1280 l S NP 2440 953 m 2559 1022 l 2440 1091 l 2440 953 l S NP 2251 1280 m 2113 1280 l 2182 1160 l 2251 1280 l S NP 2440 953 m 2302 953 l 2371 834 l 2440 953 l S NP 2302 1091 m 2440 1091 l 2371 1211 l 2302 1091 l S NP 2371 1211 m 2251 1280 l 2182 1160 l 2302 1091 l 2371 1211 l S NP 2302 1091 m 2302 953 l 2440 953 l 2440 1091 l 2302 1091 l S NP 2182 1160 m 2182 1022 l 2302 1091 l 2182 1160 l S NP 2302 953 m 2302 1091 l 2182 1022 l 2302 953 l S NP 2113 1795 m 2233 1726 l 2233 1864 l 2113 1795 l 2233 1864 l 2113 1933 l 2113 1795 l S NP 2371 1864 m 2233 1864 l 2233 1726 l 2371 1726 l 2371 1864 l S NP 2182 2053 m 2113 1933 l 2233 1864 l 2302 1984 l 2182 2053 l S NP 2233 1864 m 2371 1864 l 2302 1984 l 2233 1864 l S NP 2371 1726 m 2509 1726 l 2509 1864 l 2371 1864 l 2371 1726 l S NP 2302 1984 m 2371 2103 l 2251 2172 l 2182 2053 l 2302 1984 l S NP 2509 1864 m 2440 1984 l 2371 1864 l 2509 1864 l S NP 2371 2103 m 2302 1984 l 2440 1984 l 2371 2103 l S NP 2371 1864 m 2440 1984 l 2302 1984 l 2371 1864 l S NP 2628 1795 m 2628 1933 l 2509 1864 l 2628 1795 l S NP 2371 2241 m 2371 2103 l 2490 2172 l 2371 2241 l S NP 2440 1984 m 2509 1864 l 2628 1933 l 2559 2053 l 2440 1984 l S NP 2559 2053 m 2490 2172 l 2371 2103 l 2440 1984 l 2559 2053 l S NP 2628 1795 m 2509 1864 l 2509 1726 l 2628 1795 l S NP 2371 2241 m 2251 2172 l 2371 2103 l 2371 2241 l 2251 2172 l 2371 2103 l 2371 2241 l S NP 2302 1984 m 2371 2103 l 2251 2172 l 2182 2053 l 2302 1984 l S NP 2182 2053 m 2113 1933 l 2233 1864 l 2302 1984 l 2182 2053 l S NP 2113 1795 m 2233 1864 l 2113 1933 l 2113 1795 l S NP 2371 2241 m 2251 2310 l 2251 2172 l 2371 2241 l S NP 2113 1795 m 2113 1933 l 1993 1864 l 2113 1795 l S NP 1805 2053 m 1924 1984 l 1924 2122 l 1805 2053 l S NP 1924 1984 m 1805 2053 l 1736 1933 l 1855 1864 l 1924 1984 l S NP 2062 2499 m 1924 2499 l 1993 2379 l 2062 2499 l S NP 1924 2499 m 1855 2379 l 1993 2379 l 1924 2499 l S NP 2113 2172 m 2251 2172 l 2251 2310 l 2113 2310 l 2113 2172 l S NP 2251 2172 m 2113 2172 l 2182 2053 l 2251 2172 l S NP 2182 2053 m 2113 2172 l 2044 2053 l 2182 2053 l S NP 2113 1933 m 2182 2053 l 2044 2053 l 2113 1933 l S NP 1924 1984 m 1993 1864 l 2113 1933 l 2044 2053 l 1924 1984 l S NP 2251 2310 m 2182 2430 l 2113 2310 l 2251 2310 l S NP 1993 2241 m 1993 2379 l 1855 2379 l 1855 2241 l 1993 2241 l 1855 2241 l 1924 2122 l 1993 2241 l S NP 1855 2241 m 1736 2172 l 1805 2053 l 1924 2122 l 1855 2241 l S NP 1667 2053 m 1805 2053 l 1736 2172 l 1667 2053 l S NP 1993 1864 m 1924 1984 l 1855 1864 l 1993 1864 l S NP 2113 2172 m 2113 2310 l 1993 2241 l 2113 2172 l S NP 2044 2053 m 1924 2122 l 1924 1984 l 2044 2053 l S NP 1924 2122 m 2044 2053 l 2113 2172 l 1993 2241 l 1924 2122 l S NP 2182 2430 m 2062 2499 l 1993 2379 l 2113 2310 l 2182 2430 l S NP 1993 2379 m 1993 2241 l 2113 2310 l 1993 2379 l S NP 1667 2053 m 1736 1933 l 1805 2053 l 1667 2053 l S NP 1855 2379 m 1736 2310 l 1855 2241 l 1855 2379 l S NP 1736 2172 m 1855 2241 l 1736 2310 l 1736 2172 l S NP 2113 1795 m 2233 1726 l 2233 1864 l 2113 1795 l S NP 2371 1864 m 2233 1864 l 2233 1726 l 2371 1726 l 2371 1864 l S NP 2371 1726 m 2509 1726 l 2509 1864 l 2371 1864 l 2371 1726 l S NP 2628 1795 m 2509 1864 l 2509 1726 l 2628 1795 l S NP 2113 1795 m 2113 1657 l 2233 1726 l 2113 1795 l S NP 2628 1795 m 2509 1726 l 2628 1657 l 2628 1795 l S NP 2559 1400 m 2559 1538 l 2440 1469 l 2559 1400 l S NP 2559 1538 m 2559 1400 l 2697 1400 l 2697 1538 l 2559 1538 l S NP 2044 1400 m 2113 1280 l 2182 1400 l 2044 1400 l S NP 2113 1280 m 2251 1280 l 2182 1400 l 2113 1280 l S NP 2302 1607 m 2233 1726 l 2113 1657 l 2182 1538 l 2302 1607 l S NP 2233 1726 m 2302 1607 l 2371 1726 l 2233 1726 l S NP 2371 1726 m 2302 1607 l 2440 1607 l 2371 1726 l S NP 2509 1726 m 2371 1726 l 2440 1607 l 2509 1726 l S NP 2559 1538 m 2628 1657 l 2509 1726 l 2440 1607 l 2559 1538 l S NP 2113 1657 m 2044 1538 l 2182 1538 l 2113 1657 l S NP 2302 1469 m 2182 1400 l 2251 1280 l 2371 1349 l 2302 1469 l 2371 1349 l 2440 1469 l 2302 1469 l S NP 2371 1349 m 2490 1280 l 2559 1400 l 2440 1469 l 2371 1349 l S NP 2628 1280 m 2559 1400 l 2490 1280 l 2628 1280 l S NP 2628 1657 m 2559 1538 l 2697 1538 l 2628 1657 l S NP 2302 1607 m 2182 1538 l 2302 1469 l 2302 1607 l S NP 2440 1607 m 2440 1469 l 2559 1538 l 2440 1607 l S NP 2440 1469 m 2440 1607 l 2302 1607 l 2302 1469 l 2440 1469 l S NP 2044 1538 m 2044 1400 l 2182 1400 l 2182 1538 l 2044 1538 l S NP 2182 1400 m 2302 1469 l 2182 1538 l 2182 1400 l S NP 2628 1280 m 2697 1400 l 2559 1400 l 2628 1280 l S NP 2251 1280 m 2371 1211 l 2371 1349 l 2251 1280 l S NP 2490 1280 m 2371 1349 l 2371 1211 l 2490 1280 l S NP 1667 2053 m 1598 1933 l 1736 1933 l 1667 2053 l 1736 1933 l 1805 2053 l 1667 2053 l S NP 1736 1795 m 1736 1933 l 1598 1933 l 1598 1795 l 1736 1795 l S NP 1924 1984 m 1805 2053 l 1736 1933 l 1855 1864 l 1924 1984 l S NP 1736 1933 m 1736 1795 l 1855 1864 l 1736 1933 l S NP 1598 1795 m 1667 1676 l 1736 1795 l 1598 1795 l S NP 1924 1984 m 1855 1864 l 1993 1864 l 1924 1984 l S NP 1855 1726 m 1855 1864 l 1736 1795 l 1855 1726 l S NP 1667 1676 m 1667 1538 l 1786 1607 l 1667 1676 l S NP 1993 1864 m 1993 1726 l 2113 1795 l 1993 1864 l S NP 1786 1607 m 1924 1607 l 1855 1726 l 1786 1607 l S NP 1993 1726 m 1855 1726 l 1924 1607 l 1993 1726 l S NP 1736 1795 m 1667 1676 l 1786 1607 l 1855 1726 l 1736 1795 l S NP 1855 1726 m 1993 1726 l 1993 1864 l 1855 1864 l 1855 1726 l S NP 2113 1280 m 2182 1400 l 2044 1400 l 2113 1280 l 2044 1400 l 1975 1280 l 2113 1280 l S NP 2044 1538 m 2044 1400 l 2182 1400 l 2182 1538 l 2044 1538 l S NP 1855 1349 m 1975 1280 l 2044 1400 l 1924 1469 l 1855 1349 l S NP 2044 1400 m 2044 1538 l 1924 1469 l 2044 1400 l S NP 2182 1538 m 2113 1657 l 2044 1538 l 2182 1538 l S NP 1855 1349 m 1924 1469 l 1786 1469 l 1855 1349 l S NP 1924 1607 m 1924 1469 l 2044 1538 l 1924 1607 l S NP 2113 1657 m 2113 1795 l 1993 1726 l 2113 1657 l S NP 1786 1469 m 1786 1607 l 1667 1538 l 1786 1469 l S NP 1993 1726 m 1855 1726 l 1924 1607 l 1993 1726 l S NP 1786 1607 m 1924 1607 l 1855 1726 l 1786 1607 l S NP 2044 1538 m 2113 1657 l 1993 1726 l 1924 1607 l 2044 1538 l S NP 1924 1607 m 1786 1607 l 1786 1469 l 1924 1469 l 1924 1607 l S NP 3332 2499 m 3263 2379 l 3401 2379 l 3332 2499 l S NP 3401 2241 m 3401 2379 l 3263 2379 l 3263 2241 l 3401 2241 l S NP 3401 2379 m 3401 2241 l 3520 2310 l 3401 2379 l S NP 3263 2379 m 3143 2310 l 3263 2241 l 3263 2379 l S NP 3143 2172 m 3263 2241 l 3143 2310 l 3143 2172 l S NP 3520 2172 m 3520 2310 l 3401 2241 l 3520 2172 l S NP 3143 2172 m 3074 2053 l 3212 2053 l 3143 2172 l S NP 3520 2172 m 3451 2053 l 3589 2053 l 3520 2172 l S NP 3332 2122 m 3401 2241 l 3263 2241 l 3332 2122 l S NP 3263 2241 m 3143 2172 l 3212 2053 l 3332 2122 l 3263 2241 l S NP 3332 2122 m 3451 2053 l 3520 2172 l 3401 2241 l 3332 2122 l S NP 3212 2053 m 3332 1984 l 3332 2122 l 3212 2053 l S NP 3451 2053 m 3332 2122 l 3332 1984 l 3451 2053 l S NP 3589 1538 m 3470 1607 l 3470 1469 l 3589 1538 l S NP 3332 1469 m 3470 1469 l 3470 1607 l 3332 1607 l 3332 1469 l S NP 3332 1607 m 3194 1607 l 3194 1469 l 3332 1469 l 3332 1607 l S NP 3074 1538 m 3194 1469 l 3194 1607 l 3074 1538 l S NP 3589 1538 m 3589 1676 l 3470 1607 l 3589 1538 l S NP 3074 1538 m 3194 1607 l 3074 1676 l 3074 1538 l S NP 3143 1933 m 3143 1795 l 3263 1864 l 3143 1933 l S NP 3143 1795 m 3143 1933 l 3005 1933 l 3005 1795 l 3143 1795 l S NP 3658 1933 m 3589 2053 l 3520 1933 l 3658 1933 l S NP 3589 2053 m 3451 2053 l 3520 1933 l 3589 2053 l S NP 3401 1726 m 3470 1607 l 3589 1676 l 3520 1795 l 3401 1726 l S NP 3470 1607 m 3401 1726 l 3332 1607 l 3470 1607 l S NP 3332 1607 m 3401 1726 l 3263 1726 l 3332 1607 l S NP 3194 1607 m 3332 1607 l 3263 1726 l 3194 1607 l S NP 3143 1795 m 3074 1676 l 3194 1607 l 3263 1726 l 3143 1795 l S NP 3589 1676 m 3658 1795 l 3520 1795 l 3589 1676 l S NP 3401 1864 m 3520 1933 l 3451 2053 l 3332 1984 l 3401 1864 l 3332 1984 l 3263 1864 l 3401 1864 l S NP 3332 1984 m 3212 2053 l 3143 1933 l 3263 1864 l 3332 1984 l S NP 3074 2053 m 3143 1933 l 3212 2053 l 3074 2053 l S NP 3074 1676 m 3143 1795 l 3005 1795 l 3074 1676 l S NP 3401 1726 m 3520 1795 l 3401 1864 l 3401 1726 l S NP 3263 1726 m 3263 1864 l 3143 1795 l 3263 1726 l S NP 3263 1864 m 3263 1726 l 3401 1726 l 3401 1864 l 3263 1864 l S NP 3658 1795 m 3658 1933 l 3520 1933 l 3520 1795 l 3658 1795 l S NP 3520 1933 m 3401 1864 l 3520 1795 l 3520 1933 l S NP 3074 2053 m 3005 1933 l 3143 1933 l 3074 2053 l S NP 3451 2053 m 3332 2122 l 3332 1984 l 3451 2053 l S NP 3212 2053 m 3332 1984 l 3332 2122 l 3212 2053 l S NP 3589 2053 m 3520 1933 l 3658 1933 l 3589 2053 l 3658 1933 l 3727 2053 l 3589 2053 l S NP 3658 1795 m 3658 1933 l 3520 1933 l 3520 1795 l 3658 1795 l S NP 3847 1984 m 3727 2053 l 3658 1933 l 3778 1864 l 3847 1984 l S NP 3658 1933 m 3658 1795 l 3778 1864 l 3658 1933 l S NP 3520 1795 m 3589 1676 l 3658 1795 l 3520 1795 l S NP 3847 1984 m 3778 1864 l 3916 1864 l 3847 1984 l S NP 3778 1726 m 3778 1864 l 3658 1795 l 3778 1726 l S NP 3589 1676 m 3589 1538 l 3709 1607 l 3589 1676 l S NP 3916 1864 m 3916 1726 l 4035 1795 l 3916 1864 l S NP 3709 1607 m 3847 1607 l 3778 1726 l 3709 1607 l S NP 3916 1726 m 3778 1726 l 3847 1607 l 3916 1726 l S NP 3658 1795 m 3589 1676 l 3709 1607 l 3778 1726 l 3658 1795 l S NP 3778 1726 m 3916 1726 l 3916 1864 l 3778 1864 l 3778 1726 l S NP 3074 2053 m 2936 2053 l 3005 1933 l 3074 2053 l 3005 1933 l 3143 1933 l 3074 2053 l S NP 2886 1864 m 3005 1933 l 2936 2053 l 2817 1984 l 2886 1864 l S NP 3143 1795 m 3143 1933 l 3005 1933 l 3005 1795 l 3143 1795 l S NP 3005 1933 m 2886 1864 l 3005 1795 l 3005 1933 l S NP 2817 1984 m 2748 1864 l 2886 1864 l 2817 1984 l S NP 3143 1795 m 3005 1795 l 3074 1676 l 3143 1795 l S NP 2886 1726 m 3005 1795 l 2886 1864 l 2886 1726 l S NP 2748 1864 m 2628 1795 l 2748 1726 l 2748 1864 l S NP 3074 1676 m 2955 1607 l 3074 1538 l 3074 1676 l S NP 2748 1726 m 2817 1607 l 2886 1726 l 2748 1726 l S NP 2955 1607 m 2886 1726 l 2817 1607 l 2955 1607 l S NP 2886 1864 m 2748 1864 l 2748 1726 l 2886 1726 l 2886 1864 l S NP 2886 1726 m 2955 1607 l 3074 1676 l 3005 1795 l 2886 1726 l S NP 2628 1280 m 2766 1280 l 2697 1400 l 2628 1280 l 2697 1400 l 2559 1400 l 2628 1280 l S NP 2817 1469 m 2697 1400 l 2766 1280 l 2886 1349 l 2817 1469 l S NP 2559 1538 m 2559 1400 l 2697 1400 l 2697 1538 l 2559 1538 l S NP 2697 1400 m 2817 1469 l 2697 1538 l 2697 1400 l S NP 2886 1349 m 2955 1469 l 2817 1469 l 2886 1349 l S NP 2559 1538 m 2697 1538 l 2628 1657 l 2559 1538 l S NP 2817 1607 m 2697 1538 l 2817 1469 l 2817 1607 l S NP 2955 1469 m 3074 1538 l 2955 1607 l 2955 1469 l S NP 2628 1657 m 2748 1726 l 2628 1795 l 2628 1657 l S NP 2955 1607 m 2886 1726 l 2817 1607 l 2955 1607 l S NP 2748 1726 m 2817 1607 l 2886 1726 l 2748 1726 l S NP 2817 1469 m 2955 1469 l 2955 1607 l 2817 1607 l 2817 1469 l S NP 2817 1607 m 2748 1726 l 2628 1657 l 2697 1538 l 2817 1607 l S NP 4035 1280 m 4104 1400 l 3966 1400 l 4035 1280 l 3966 1400 l 3897 1280 l 4035 1280 l S NP 3966 1538 m 3966 1400 l 4104 1400 l 4104 1538 l 3966 1538 l S NP 3778 1349 m 3897 1280 l 3966 1400 l 3847 1469 l 3778 1349 l S NP 3966 1400 m 3966 1538 l 3847 1469 l 3966 1400 l S NP 4104 1538 m 4035 1657 l 3966 1538 l 4104 1538 l S NP 3778 1349 m 3847 1469 l 3709 1469 l 3778 1349 l S NP 3847 1607 m 3847 1469 l 3966 1538 l 3847 1607 l S NP 4035 1657 m 4035 1795 l 3916 1726 l 4035 1657 l S NP 3709 1469 m 3709 1607 l 3589 1538 l 3709 1469 l S NP 3916 1726 m 3778 1726 l 3847 1607 l 3916 1726 l S NP 3709 1607 m 3847 1607 l 3778 1726 l 3709 1607 l S NP 3966 1538 m 4035 1657 l 3916 1726 l 3847 1607 l 3966 1538 l S NP 3847 1607 m 3709 1607 l 3709 1469 l 3847 1469 l 3847 1607 l S NP 2628 1280 m 2559 1160 l 2697 1160 l 2628 1280 l S NP 2697 1022 m 2697 1160 l 2559 1160 l 2559 1022 l 2697 1022 l S NP 2697 1160 m 2697 1022 l 2817 1091 l 2697 1160 l S NP 2559 1160 m 2440 1091 l 2559 1022 l 2559 1160 l S NP 2440 953 m 2559 1022 l 2440 1091 l 2440 953 l S NP 2817 953 m 2817 1091 l 2697 1022 l 2817 953 l S NP 2440 953 m 2371 834 l 2509 834 l 2440 953 l S NP 2817 953 m 2748 834 l 2886 834 l 2817 953 l S NP 2628 903 m 2697 1022 l 2559 1022 l 2628 903 l S NP 2559 1022 m 2440 953 l 2509 834 l 2628 903 l 2559 1022 l S NP 2628 903 m 2748 834 l 2817 953 l 2697 1022 l 2628 903 l S NP 2509 834 m 2628 765 l 2628 903 l 2509 834 l S NP 2748 834 m 2628 903 l 2628 765 l 2748 834 l S NP 4035 1280 m 3966 1160 l 4104 1160 l 4035 1280 l S NP 4104 1022 m 4104 1160 l 3966 1160 l 3966 1022 l 4104 1022 l S NP 4104 1160 m 4104 1022 l 4224 1091 l 4104 1160 l S NP 3966 1160 m 3847 1091 l 3966 1022 l 3966 1160 l S NP 3847 953 m 3966 1022 l 3847 1091 l 3847 953 l S NP 4224 953 m 4224 1091 l 4104 1022 l 4224 953 l S NP 3847 953 m 3778 834 l 3916 834 l 3847 953 l S NP 4224 953 m 4155 834 l 4293 834 l 4224 953 l S NP 4035 903 m 4104 1022 l 3966 1022 l 4035 903 l S NP 3966 1022 m 3847 953 l 3916 834 l 4035 903 l 3966 1022 l S NP 4035 903 m 4155 834 l 4224 953 l 4104 1022 l 4035 903 l S NP 3916 834 m 4035 765 l 4035 903 l 3916 834 l S NP 4155 834 m 4035 903 l 4035 765 l 4155 834 l S NP 3332 1091 m 3451 1160 l 3332 1229 l 3332 1091 l 3332 1229 l 3212 1160 l 3332 1091 l S NP 3401 1349 m 3332 1229 l 3451 1160 l 3520 1280 l 3401 1349 l S NP 3143 1280 m 3212 1160 l 3332 1229 l 3263 1349 l 3143 1280 l S NP 3332 1229 m 3401 1349 l 3263 1349 l 3332 1229 l S NP 3520 1280 m 3589 1400 l 3470 1469 l 3401 1349 l 3520 1280 l S NP 3263 1349 m 3194 1469 l 3074 1400 l 3143 1280 l 3263 1349 l S NP 3470 1469 m 3332 1469 l 3401 1349 l 3470 1469 l S NP 3194 1469 m 3263 1349 l 3332 1469 l 3194 1469 l S NP 3401 1349 m 3332 1469 l 3263 1349 l 3401 1349 l S NP 3589 1538 m 3470 1607 l 3470 1469 l 3589 1538 l S NP 3074 1538 m 3194 1469 l 3194 1607 l 3074 1538 l S NP 3332 1469 m 3470 1469 l 3470 1607 l 3332 1607 l 3332 1469 l S NP 3332 1607 m 3194 1607 l 3194 1469 l 3332 1469 l 3332 1607 l S NP 3589 1538 m 3470 1469 l 3589 1400 l 3589 1538 l S NP 3074 1538 m 3074 1400 l 3194 1469 l 3074 1538 l 3074 1400 l 3194 1469 l 3074 1538 l S NP 3263 1349 m 3194 1469 l 3074 1400 l 3143 1280 l 3263 1349 l S NP 3143 1280 m 3212 1160 l 3332 1229 l 3263 1349 l 3143 1280 l S NP 3332 1091 m 3332 1229 l 3212 1160 l 3332 1091 l S NP 3074 1538 m 2955 1469 l 3074 1400 l 3074 1538 l S NP 3332 1091 m 3212 1160 l 3212 1022 l 3332 1091 l S NP 2955 953 m 3074 1022 l 2955 1091 l 2955 953 l S NP 3074 1022 m 2955 953 l 3024 834 l 3143 903 l 3074 1022 l S NP 2697 1400 m 2628 1280 l 2766 1280 l 2697 1400 l S NP 2628 1280 m 2697 1160 l 2766 1280 l 2628 1280 l S NP 3005 1280 m 3074 1400 l 2955 1469 l 2886 1349 l 3005 1280 l S NP 3074 1400 m 3005 1280 l 3143 1280 l 3074 1400 l S NP 3143 1280 m 3005 1280 l 3074 1160 l 3143 1280 l S NP 3212 1160 m 3143 1280 l 3074 1160 l 3212 1160 l S NP 3074 1022 m 3212 1022 l 3212 1160 l 3074 1160 l 3074 1022 l S NP 2955 1469 m 2817 1469 l 2886 1349 l 2955 1469 l S NP 2886 1211 m 2766 1280 l 2697 1160 l 2817 1091 l 2886 1211 l 2817 1091 l 2955 1091 l 2886 1211 l S NP 2817 1091 m 2817 953 l 2955 953 l 2955 1091 l 2817 1091 l S NP 2886 834 m 2955 953 l 2817 953 l 2886 834 l S NP 3212 1022 m 3074 1022 l 3143 903 l 3212 1022 l S NP 3005 1280 m 2886 1349 l 2886 1211 l 3005 1280 l S NP 3074 1160 m 2955 1091 l 3074 1022 l 3074 1160 l S NP 2955 1091 m 3074 1160 l 3005 1280 l 2886 1211 l 2955 1091 l S NP 2817 1469 m 2697 1400 l 2766 1280 l 2886 1349 l 2817 1469 l S NP 2766 1280 m 2886 1211 l 2886 1349 l 2766 1280 l S NP 2886 834 m 3024 834 l 2955 953 l 2886 834 l S NP 2697 1160 m 2697 1022 l 2817 1091 l 2697 1160 l S NP 2817 953 m 2817 1091 l 2697 1022 l 2817 953 l S NP 3332 1091 m 3451 1160 l 3332 1229 l 3332 1091 l S NP 3401 1349 m 3332 1229 l 3451 1160 l 3520 1280 l 3401 1349 l S NP 3520 1280 m 3589 1400 l 3470 1469 l 3401 1349 l 3520 1280 l S NP 3589 1538 m 3470 1469 l 3589 1400 l 3589 1538 l S NP 3332 1091 m 3451 1022 l 3451 1160 l 3332 1091 l S NP 3589 1538 m 3589 1400 l 3709 1469 l 3589 1538 l S NP 3897 1280 m 3778 1349 l 3778 1211 l 3897 1280 l S NP 3778 1349 m 3897 1280 l 3966 1400 l 3847 1469 l 3778 1349 l S NP 3640 834 m 3778 834 l 3709 953 l 3640 834 l S NP 3778 834 m 3847 953 l 3709 953 l 3778 834 l S NP 3589 1160 m 3451 1160 l 3451 1022 l 3589 1022 l 3589 1160 l S NP 3451 1160 m 3589 1160 l 3520 1280 l 3451 1160 l S NP 3520 1280 m 3589 1160 l 3658 1280 l 3520 1280 l S NP 3589 1400 m 3520 1280 l 3658 1280 l 3589 1400 l S NP 3778 1349 m 3709 1469 l 3589 1400 l 3658 1280 l 3778 1349 l S NP 3451 1022 m 3520 903 l 3589 1022 l 3451 1022 l S NP 3709 1091 m 3709 953 l 3847 953 l 3847 1091 l 3709 1091 l 3847 1091 l 3778 1211 l 3709 1091 l S NP 3847 1091 m 3966 1160 l 3897 1280 l 3778 1211 l 3847 1091 l S NP 4035 1280 m 3897 1280 l 3966 1160 l 4035 1280 l S NP 3709 1469 m 3778 1349 l 3847 1469 l 3709 1469 l S NP 3589 1160 m 3589 1022 l 3709 1091 l 3589 1160 l S NP 3658 1280 m 3778 1211 l 3778 1349 l 3658 1280 l S NP 3778 1211 m 3658 1280 l 3589 1160 l 3709 1091 l 3778 1211 l S NP 3520 903 m 3640 834 l 3709 953 l 3589 1022 l 3520 903 l S NP 3709 953 m 3709 1091 l 3589 1022 l 3709 953 l S NP 4035 1280 m 3966 1400 l 3897 1280 l 4035 1280 l S NP 3847 953 m 3966 1022 l 3847 1091 l 3847 953 l S NP 3966 1160 m 3847 1091 l 3966 1022 l 3966 1160 l S NP 2886 834 m 2955 714 l 3024 834 l 2886 834 l 3024 834 l 2955 953 l 2886 834 l S NP 3143 765 m 3024 834 l 2955 714 l 3074 645 l 3143 765 l S NP 3074 1022 m 2955 953 l 3024 834 l 3143 903 l 3074 1022 l S NP 3024 834 m 3143 765 l 3143 903 l 3024 834 l S NP 3074 645 m 3212 645 l 3143 765 l 3074 645 l S NP 3074 1022 m 3143 903 l 3212 1022 l 3074 1022 l S NP 3263 834 m 3143 903 l 3143 765 l 3263 834 l S NP 3212 645 m 3332 576 l 3332 714 l 3212 645 l S NP 3212 1022 m 3332 953 l 3332 1091 l 3212 1022 l S NP 3332 714 m 3401 834 l 3263 834 l 3332 714 l S NP 3332 953 m 3263 834 l 3401 834 l 3332 953 l S NP 3143 765 m 3212 645 l 3332 714 l 3263 834 l 3143 765 l S NP 3263 834 m 3332 953 l 3212 1022 l 3143 903 l 3263 834 l S NP 3778 834 m 3709 953 l 3640 834 l 3778 834 l 3640 834 l 3709 714 l 3778 834 l S NP 3520 903 m 3640 834 l 3709 953 l 3589 1022 l 3520 903 l S NP 3589 645 m 3709 714 l 3640 834 l 3520 765 l 3589 645 l S NP 3640 834 m 3520 903 l 3520 765 l 3640 834 l S NP 3589 1022 m 3451 1022 l 3520 903 l 3589 1022 l S NP 3589 645 m 3520 765 l 3451 645 l 3589 645 l S NP 3401 834 m 3520 765 l 3520 903 l 3401 834 l S NP 3451 1022 m 3332 1091 l 3332 953 l 3451 1022 l S NP 3451 645 m 3332 714 l 3332 576 l 3451 645 l S NP 3332 953 m 3263 834 l 3401 834 l 3332 953 l S NP 3332 714 m 3401 834 l 3263 834 l 3332 714 l S NP 3520 903 m 3451 1022 l 3332 953 l 3401 834 l 3520 903 l S NP 3401 834 m 3332 714 l 3451 645 l 3520 765 l 3401 834 l S NP 3332 2499 m 3401 2379 l 3470 2499 l 3332 2499 l S NP 3589 2430 m 3470 2499 l 3401 2379 l 3520 2310 l 3589 2430 l S NP 3470 2499 m 3589 2430 l 3589 2568 l 3470 2499 l S NP 3401 2379 m 3401 2241 l 3520 2310 l 3401 2379 l S NP 3520 2172 m 3520 2310 l 3401 2241 l 3520 2172 l S NP 3709 2499 m 3589 2568 l 3589 2430 l 3709 2499 l S NP 3520 2172 m 3589 2053 l 3658 2172 l 3520 2172 l S NP 3709 2499 m 3778 2379 l 3847 2499 l 3709 2499 l S NP 3658 2310 m 3589 2430 l 3520 2310 l 3658 2310 l S NP 3520 2310 m 3520 2172 l 3658 2172 l 3658 2310 l 3520 2310 l S NP 3658 2310 m 3778 2379 l 3709 2499 l 3589 2430 l 3658 2310 l S NP 3658 2172 m 3778 2241 l 3658 2310 l 3658 2172 l S NP 3778 2379 m 3658 2310 l 3778 2241 l 3778 2379 l S NP 4293 2241 m 4173 2172 l 4293 2103 l 4293 2241 l S NP 4224 1984 m 4293 2103 l 4173 2172 l 4104 2053 l 4224 1984 l S NP 4104 2053 m 4035 1933 l 4155 1864 l 4224 1984 l 4104 2053 l S NP 4035 1795 m 4155 1864 l 4035 1933 l 4035 1795 l S NP 4293 2241 m 4173 2310 l 4173 2172 l 4293 2241 l S NP 4035 1795 m 4035 1933 l 3916 1864 l 4035 1795 l S NP 3727 2053 m 3847 1984 l 3847 2122 l 3727 2053 l S NP 3847 1984 m 3727 2053 l 3658 1933 l 3778 1864 l 3847 1984 l S NP 3985 2499 m 3847 2499 l 3916 2379 l 3985 2499 l S NP 3847 2499 m 3778 2379 l 3916 2379 l 3847 2499 l S NP 4035 2172 m 4173 2172 l 4173 2310 l 4035 2310 l 4035 2172 l S NP 4173 2172 m 4035 2172 l 4104 2053 l 4173 2172 l S NP 4104 2053 m 4035 2172 l 3966 2053 l 4104 2053 l S NP 4035 1933 m 4104 2053 l 3966 2053 l 4035 1933 l S NP 3847 1984 m 3916 1864 l 4035 1933 l 3966 2053 l 3847 1984 l S NP 4173 2310 m 4104 2430 l 4035 2310 l 4173 2310 l S NP 3916 2241 m 3916 2379 l 3778 2379 l 3778 2241 l 3916 2241 l 3778 2241 l 3847 2122 l 3916 2241 l S NP 3778 2241 m 3658 2172 l 3727 2053 l 3847 2122 l 3778 2241 l S NP 3589 2053 m 3727 2053 l 3658 2172 l 3589 2053 l S NP 3916 1864 m 3847 1984 l 3778 1864 l 3916 1864 l S NP 4035 2172 m 4035 2310 l 3916 2241 l 4035 2172 l S NP 3966 2053 m 3847 2122 l 3847 1984 l 3966 2053 l S NP 3847 2122 m 3966 2053 l 4035 2172 l 3916 2241 l 3847 2122 l S NP 4104 2430 m 3985 2499 l 3916 2379 l 4035 2310 l 4104 2430 l S NP 3916 2379 m 3916 2241 l 4035 2310 l 3916 2379 l S NP 3589 2053 m 3658 1933 l 3727 2053 l 3589 2053 l S NP 3778 2379 m 3658 2310 l 3778 2241 l 3778 2379 l S NP 3658 2172 m 3778 2241 l 3658 2310 l 3658 2172 l S NP 3847 2499 m 3916 2379 l 3985 2499 l 3847 2499 l 3985 2499 l 3916 2618 l 3847 2499 l S NP 4104 2430 m 3985 2499 l 3916 2379 l 4035 2310 l 4104 2430 l S NP 4035 2687 m 3916 2618 l 3985 2499 l 4104 2568 l 4035 2687 l S NP 3985 2499 m 4104 2430 l 4104 2568 l 3985 2499 l S NP 4035 2310 m 4173 2310 l 4104 2430 l 4035 2310 l S NP 4035 2687 m 4104 2568 l 4173 2687 l 4035 2687 l S NP 4224 2499 m 4104 2568 l 4104 2430 l 4224 2499 l S NP 4173 2310 m 4293 2241 l 4293 2379 l 4173 2310 l S NP 4173 2687 m 4293 2618 l 4293 2756 l 4173 2687 l S NP 4293 2379 m 4362 2499 l 4224 2499 l 4293 2379 l S NP 4293 2618 m 4224 2499 l 4362 2499 l 4293 2618 l S NP 4104 2430 m 4173 2310 l 4293 2379 l 4224 2499 l 4104 2430 l S NP 4224 2499 m 4293 2618 l 4173 2687 l 4104 2568 l 4224 2499 l S NP 3589 2053 m 3520 1933 l 3658 1933 l 3589 2053 l 3658 1933 l 3727 2053 l 3589 2053 l S NP 3658 1795 m 3658 1933 l 3520 1933 l 3520 1795 l 3658 1795 l S NP 3847 1984 m 3727 2053 l 3658 1933 l 3778 1864 l 3847 1984 l S NP 3658 1933 m 3658 1795 l 3778 1864 l 3658 1933 l S NP 3520 1795 m 3589 1676 l 3658 1795 l 3520 1795 l S NP 3847 1984 m 3778 1864 l 3916 1864 l 3847 1984 l S NP 3778 1726 m 3778 1864 l 3658 1795 l 3778 1726 l S NP 3589 1676 m 3589 1538 l 3709 1607 l 3589 1676 l S NP 3916 1864 m 3916 1726 l 4035 1795 l 3916 1864 l S NP 3709 1607 m 3847 1607 l 3778 1726 l 3709 1607 l S NP 3916 1726 m 3778 1726 l 3847 1607 l 3916 1726 l S NP 3658 1795 m 3589 1676 l 3709 1607 l 3778 1726 l 3658 1795 l S NP 3778 1726 m 3916 1726 l 3916 1864 l 3778 1864 l 3778 1726 l S NP 4035 1280 m 4104 1400 l 3966 1400 l 4035 1280 l 3966 1400 l 3897 1280 l 4035 1280 l S NP 3966 1538 m 3966 1400 l 4104 1400 l 4104 1538 l 3966 1538 l S NP 3778 1349 m 3897 1280 l 3966 1400 l 3847 1469 l 3778 1349 l S NP 3966 1400 m 3966 1538 l 3847 1469 l 3966 1400 l S NP 4104 1538 m 4035 1657 l 3966 1538 l 4104 1538 l S NP 3778 1349 m 3847 1469 l 3709 1469 l 3778 1349 l S NP 3847 1607 m 3847 1469 l 3966 1538 l 3847 1607 l S NP 4035 1657 m 4035 1795 l 3916 1726 l 4035 1657 l S NP 3709 1469 m 3709 1607 l 3589 1538 l 3709 1469 l S NP 3916 1726 m 3778 1726 l 3847 1607 l 3916 1726 l S NP 3709 1607 m 3847 1607 l 3778 1726 l 3709 1607 l S NP 3966 1538 m 4035 1657 l 3916 1726 l 3847 1607 l 3966 1538 l S NP 3847 1607 m 3709 1607 l 3709 1469 l 3847 1469 l 3847 1607 l S NP 4739 2499 m 4670 2618 l 4601 2499 l 4739 2499 l 4601 2499 l 4670 2379 l 4739 2499 l S NP 4481 2568 m 4601 2499 l 4670 2618 l 4550 2687 l 4481 2568 l S NP 4550 2310 m 4670 2379 l 4601 2499 l 4481 2430 l 4550 2310 l S NP 4601 2499 m 4481 2568 l 4481 2430 l 4601 2499 l S NP 4550 2687 m 4412 2687 l 4481 2568 l 4550 2687 l S NP 4550 2310 m 4481 2430 l 4412 2310 l 4550 2310 l S NP 4362 2499 m 4481 2430 l 4481 2568 l 4362 2499 l S NP 4412 2687 m 4293 2756 l 4293 2618 l 4412 2687 l S NP 4412 2310 m 4293 2379 l 4293 2241 l 4412 2310 l S NP 4293 2618 m 4224 2499 l 4362 2499 l 4293 2618 l S NP 4293 2379 m 4362 2499 l 4224 2499 l 4293 2379 l S NP 4481 2568 m 4412 2687 l 4293 2618 l 4362 2499 l 4481 2568 l S NP 4362 2499 m 4293 2379 l 4412 2310 l 4481 2430 l 4362 2499 l S NP 4035 1280 m 4104 1160 l 4173 1280 l 4035 1280 l S NP 4293 1211 m 4173 1280 l 4104 1160 l 4224 1091 l 4293 1211 l S NP 4173 1280 m 4293 1211 l 4293 1349 l 4173 1280 l S NP 4104 1160 m 4104 1022 l 4224 1091 l 4104 1160 l S NP 4224 953 m 4224 1091 l 4104 1022 l 4224 953 l S NP 4412 1280 m 4293 1349 l 4293 1211 l 4412 1280 l S NP 4224 953 m 4293 834 l 4362 953 l 4224 953 l S NP 4412 1280 m 4481 1160 l 4550 1280 l 4412 1280 l S NP 4362 1091 m 4293 1211 l 4224 1091 l 4362 1091 l S NP 4224 1091 m 4224 953 l 4362 953 l 4362 1091 l 4224 1091 l S NP 4362 1091 m 4481 1160 l 4412 1280 l 4293 1211 l 4362 1091 l S NP 4362 953 m 4481 1022 l 4362 1091 l 4362 953 l S NP 4481 1160 m 4362 1091 l 4481 1022 l 4481 1160 l S NP 4739 2499 m 4808 2379 l 4877 2499 l 4739 2499 l S NP 4997 2430 m 4877 2499 l 4808 2379 l 4928 2310 l 4997 2430 l S NP 4877 2499 m 4997 2430 l 4997 2568 l 4877 2499 l S NP 4808 2379 m 4808 2241 l 4928 2310 l 4808 2379 l S NP 4928 2172 m 4928 2310 l 4808 2241 l 4928 2172 l S NP 5116 2499 m 4997 2568 l 4997 2430 l 5116 2499 l S NP 4928 2172 m 4997 2053 l 5066 2172 l 4928 2172 l S NP 5116 2499 m 5185 2379 l 5254 2499 l 5116 2499 l S NP 5066 2310 m 4997 2430 l 4928 2310 l 5066 2310 l S NP 4928 2310 m 4928 2172 l 5066 2172 l 5066 2310 l 4928 2310 l S NP 5066 2310 m 5185 2379 l 5116 2499 l 4997 2430 l 5066 2310 l S NP 5066 2172 m 5185 2241 l 5066 2310 l 5066 2172 l S NP 5185 2379 m 5066 2310 l 5185 2241 l 5185 2379 l S NP 4550 1795 m 4550 1933 l 4431 1864 l 4550 1795 l 4431 1864 l 4431 1726 l 4550 1795 l S NP 4362 1984 m 4431 1864 l 4550 1933 l 4481 2053 l 4362 1984 l S NP 4293 1726 m 4431 1726 l 4431 1864 l 4293 1864 l 4293 1726 l S NP 4431 1864 m 4362 1984 l 4293 1864 l 4431 1864 l S NP 4481 2053 m 4412 2172 l 4293 2103 l 4362 1984 l 4481 2053 l S NP 4293 1864 m 4155 1864 l 4155 1726 l 4293 1726 l 4293 1864 l S NP 4293 2103 m 4224 1984 l 4362 1984 l 4293 2103 l S NP 4155 1864 m 4293 1864 l 4224 1984 l 4155 1864 l S NP 4362 1984 m 4224 1984 l 4293 1864 l 4362 1984 l S NP 4293 2241 m 4173 2172 l 4293 2103 l 4293 2241 l S NP 4035 1795 m 4155 1864 l 4035 1933 l 4035 1795 l S NP 4224 1984 m 4293 2103 l 4173 2172 l 4104 2053 l 4224 1984 l S NP 4104 2053 m 4035 1933 l 4155 1864 l 4224 1984 l 4104 2053 l S NP 4293 2241 m 4293 2103 l 4412 2172 l 4293 2241 l S NP 4035 1795 m 4155 1726 l 4155 1864 l 4035 1795 l 4155 1726 l 4155 1864 l 4035 1795 l S NP 4293 1864 m 4155 1864 l 4155 1726 l 4293 1726 l 4293 1864 l S NP 4293 1726 m 4431 1726 l 4431 1864 l 4293 1864 l 4293 1726 l S NP 4550 1795 m 4431 1864 l 4431 1726 l 4550 1795 l S NP 4035 1795 m 4035 1657 l 4155 1726 l 4035 1795 l S NP 4550 1795 m 4431 1726 l 4550 1657 l 4550 1795 l S NP 4481 1400 m 4481 1538 l 4362 1469 l 4481 1400 l S NP 4481 1538 m 4481 1400 l 4619 1400 l 4619 1538 l 4481 1538 l S NP 3966 1400 m 4035 1280 l 4104 1400 l 3966 1400 l S NP 4035 1280 m 4173 1280 l 4104 1400 l 4035 1280 l S NP 4224 1607 m 4155 1726 l 4035 1657 l 4104 1538 l 4224 1607 l S NP 4155 1726 m 4224 1607 l 4293 1726 l 4155 1726 l S NP 4293 1726 m 4224 1607 l 4362 1607 l 4293 1726 l S NP 4431 1726 m 4293 1726 l 4362 1607 l 4431 1726 l S NP 4481 1538 m 4550 1657 l 4431 1726 l 4362 1607 l 4481 1538 l S NP 4035 1657 m 3966 1538 l 4104 1538 l 4035 1657 l S NP 4224 1469 m 4104 1400 l 4173 1280 l 4293 1349 l 4224 1469 l 4293 1349 l 4362 1469 l 4224 1469 l S NP 4293 1349 m 4412 1280 l 4481 1400 l 4362 1469 l 4293 1349 l S NP 4550 1280 m 4481 1400 l 4412 1280 l 4550 1280 l S NP 4550 1657 m 4481 1538 l 4619 1538 l 4550 1657 l S NP 4224 1607 m 4104 1538 l 4224 1469 l 4224 1607 l S NP 4362 1607 m 4362 1469 l 4481 1538 l 4362 1607 l S NP 4362 1469 m 4362 1607 l 4224 1607 l 4224 1469 l 4362 1469 l S NP 3966 1538 m 3966 1400 l 4104 1400 l 4104 1538 l 3966 1538 l S NP 4104 1400 m 4224 1469 l 4104 1538 l 4104 1400 l S NP 4550 1280 m 4619 1400 l 4481 1400 l 4550 1280 l S NP 4173 1280 m 4293 1211 l 4293 1349 l 4173 1280 l S NP 4412 1280 m 4293 1349 l 4293 1211 l 4412 1280 l S NP 4550 1795 m 4550 1933 l 4431 1864 l 4550 1795 l S NP 4362 1984 m 4431 1864 l 4550 1933 l 4481 2053 l 4362 1984 l S NP 4481 2053 m 4412 2172 l 4293 2103 l 4362 1984 l 4481 2053 l S NP 4293 2241 m 4293 2103 l 4412 2172 l 4293 2241 l S NP 4550 1795 m 4670 1864 l 4550 1933 l 4550 1795 l S NP 4293 2241 m 4412 2172 l 4412 2310 l 4293 2241 l S NP 4670 2379 m 4550 2310 l 4670 2241 l 4670 2379 l S NP 4550 2310 m 4670 2379 l 4601 2499 l 4481 2430 l 4550 2310 l S NP 4928 1933 m 4997 2053 l 4859 2053 l 4928 1933 l S NP 4997 2053 m 4928 2172 l 4859 2053 l 4997 2053 l S NP 4619 2053 m 4550 1933 l 4670 1864 l 4739 1984 l 4619 2053 l S NP 4550 1933 m 4619 2053 l 4481 2053 l 4550 1933 l S NP 4481 2053 m 4619 2053 l 4550 2172 l 4481 2053 l S NP 4412 2172 m 4481 2053 l 4550 2172 l 4412 2172 l S NP 4550 2310 m 4412 2310 l 4412 2172 l 4550 2172 l 4550 2310 l S NP 4670 1864 m 4808 1864 l 4739 1984 l 4670 1864 l S NP 4739 2122 m 4859 2053 l 4928 2172 l 4808 2241 l 4739 2122 l 4808 2241 l 4670 2241 l 4739 2122 l S NP 4808 2241 m 4808 2379 l 4670 2379 l 4670 2241 l 4808 2241 l S NP 4739 2499 m 4670 2379 l 4808 2379 l 4739 2499 l S NP 4412 2310 m 4550 2310 l 4481 2430 l 4412 2310 l S NP 4619 2053 m 4739 1984 l 4739 2122 l 4619 2053 l S NP 4550 2172 m 4670 2241 l 4550 2310 l 4550 2172 l S NP 4670 2241 m 4550 2172 l 4619 2053 l 4739 2122 l 4670 2241 l S NP 4808 1864 m 4928 1933 l 4859 2053 l 4739 1984 l 4808 1864 l S NP 4859 2053 m 4739 2122 l 4739 1984 l 4859 2053 l S NP 4739 2499 m 4601 2499 l 4670 2379 l 4739 2499 l S NP 4928 2172 m 4928 2310 l 4808 2241 l 4928 2172 l S NP 4808 2379 m 4808 2241 l 4928 2310 l 4808 2379 l S NP 4550 1280 m 4688 1280 l 4619 1400 l 4550 1280 l 4619 1400 l 4481 1400 l 4550 1280 l S NP 4739 1469 m 4619 1400 l 4688 1280 l 4808 1349 l 4739 1469 l S NP 4481 1538 m 4481 1400 l 4619 1400 l 4619 1538 l 4481 1538 l S NP 4619 1400 m 4739 1469 l 4619 1538 l 4619 1400 l S NP 4808 1349 m 4877 1469 l 4739 1469 l 4808 1349 l S NP 4481 1538 m 4619 1538 l 4550 1657 l 4481 1538 l S NP 4739 1607 m 4619 1538 l 4739 1469 l 4739 1607 l S NP 4877 1469 m 4997 1538 l 4877 1607 l 4877 1469 l S NP 4550 1657 m 4670 1726 l 4550 1795 l 4550 1657 l S NP 4877 1607 m 4808 1726 l 4739 1607 l 4877 1607 l S NP 4670 1726 m 4739 1607 l 4808 1726 l 4670 1726 l S NP 4739 1469 m 4877 1469 l 4877 1607 l 4739 1607 l 4739 1469 l S NP 4739 1607 m 4670 1726 l 4550 1657 l 4619 1538 l 4739 1607 l S NP 4997 2053 m 4859 2053 l 4928 1933 l 4997 2053 l 4928 1933 l 5066 1933 l 4997 2053 l S NP 4808 1864 m 4928 1933 l 4859 2053 l 4739 1984 l 4808 1864 l S NP 5066 1795 m 5066 1933 l 4928 1933 l 4928 1795 l 5066 1795 l S NP 4928 1933 m 4808 1864 l 4928 1795 l 4928 1933 l S NP 4739 1984 m 4670 1864 l 4808 1864 l 4739 1984 l S NP 5066 1795 m 4928 1795 l 4997 1676 l 5066 1795 l S NP 4808 1726 m 4928 1795 l 4808 1864 l 4808 1726 l S NP 4670 1864 m 4550 1795 l 4670 1726 l 4670 1864 l S NP 4997 1676 m 4877 1607 l 4997 1538 l 4997 1676 l S NP 4670 1726 m 4739 1607 l 4808 1726 l 4670 1726 l S NP 4877 1607 m 4808 1726 l 4739 1607 l 4877 1607 l S NP 4808 1864 m 4670 1864 l 4670 1726 l 4808 1726 l 4808 1864 l S NP 4808 1726 m 4877 1607 l 4997 1676 l 4928 1795 l 4808 1726 l S NP 3332 2499 m 3470 2499 l 3401 2618 l 3332 2499 l S NP 3520 2687 m 3401 2618 l 3470 2499 l 3589 2568 l 3520 2687 l S NP 3401 2618 m 3520 2687 l 3401 2756 l 3401 2618 l S NP 3470 2499 m 3589 2430 l 3589 2568 l 3470 2499 l S NP 3709 2499 m 3589 2568 l 3589 2430 l 3709 2499 l S NP 3520 2825 m 3401 2756 l 3520 2687 l 3520 2825 l S NP 3709 2499 m 3847 2499 l 3778 2618 l 3709 2499 l S NP 3520 2825 m 3658 2825 l 3589 2945 l 3520 2825 l S NP 3658 2687 m 3520 2687 l 3589 2568 l 3658 2687 l S NP 3589 2568 m 3709 2499 l 3778 2618 l 3658 2687 l 3589 2568 l S NP 3658 2687 m 3658 2825 l 3520 2825 l 3520 2687 l 3658 2687 l S NP 3778 2618 m 3778 2756 l 3658 2687 l 3778 2618 l S NP 3658 2825 m 3658 2687 l 3778 2756 l 3658 2825 l S NP 4035 3202 m 4035 3064 l 4155 3133 l 4035 3202 l S NP 4224 3014 m 4155 3133 l 4035 3064 l 4104 2945 l 4224 3014 l S NP 4104 2945 m 4173 2825 l 4293 2894 l 4224 3014 l 4104 2945 l S NP 4293 2756 m 4293 2894 l 4173 2825 l 4293 2756 l S NP 4035 3202 m 3916 3133 l 4035 3064 l 4035 3202 l S NP 4293 2756 m 4173 2825 l 4173 2687 l 4293 2756 l S NP 3916 2618 m 4035 2687 l 3916 2756 l 3916 2618 l S NP 4035 2687 m 3916 2618 l 3985 2499 l 4104 2568 l 4035 2687 l S NP 3658 3064 m 3589 2945 l 3727 2945 l 3658 3064 l S NP 3589 2945 m 3658 2825 l 3727 2945 l 3589 2945 l S NP 3966 2945 m 4035 3064 l 3916 3133 l 3847 3014 l 3966 2945 l S NP 4035 3064 m 3966 2945 l 4104 2945 l 4035 3064 l S NP 4104 2945 m 3966 2945 l 4035 2825 l 4104 2945 l S NP 4173 2825 m 4104 2945 l 4035 2825 l 4173 2825 l S NP 4035 2687 m 4173 2687 l 4173 2825 l 4035 2825 l 4035 2687 l S NP 3916 3133 m 3778 3133 l 3847 3014 l 3916 3133 l S NP 3847 2876 m 3727 2945 l 3658 2825 l 3778 2756 l 3847 2876 l 3778 2756 l 3916 2756 l 3847 2876 l S NP 3778 2756 m 3778 2618 l 3916 2618 l 3916 2756 l 3778 2756 l S NP 3847 2499 m 3916 2618 l 3778 2618 l 3847 2499 l S NP 4173 2687 m 4035 2687 l 4104 2568 l 4173 2687 l S NP 3966 2945 m 3847 3014 l 3847 2876 l 3966 2945 l S NP 4035 2825 m 3916 2756 l 4035 2687 l 4035 2825 l S NP 3916 2756 m 4035 2825 l 3966 2945 l 3847 2876 l 3916 2756 l S NP 3778 3133 m 3658 3064 l 3727 2945 l 3847 3014 l 3778 3133 l S NP 3727 2945 m 3847 2876 l 3847 3014 l 3727 2945 l S NP 3847 2499 m 3985 2499 l 3916 2618 l 3847 2499 l S NP 3658 2825 m 3658 2687 l 3778 2756 l 3658 2825 l S NP 3778 2618 m 3778 2756 l 3658 2687 l 3778 2618 l S NP 3589 2945 m 3727 2945 l 3658 3064 l 3589 2945 l 3658 3064 l 3520 3064 l 3589 2945 l S NP 3778 3133 m 3658 3064 l 3727 2945 l 3847 3014 l 3778 3133 l S NP 3520 3202 m 3520 3064 l 3658 3064 l 3658 3202 l 3520 3202 l S NP 3658 3064 m 3778 3133 l 3658 3202 l 3658 3064 l S NP 3847 3014 m 3916 3133 l 3778 3133 l 3847 3014 l S NP 3520 3202 m 3658 3202 l 3589 3322 l 3520 3202 l S NP 3778 3271 m 3658 3202 l 3778 3133 l 3778 3271 l S NP 3916 3133 m 4035 3202 l 3916 3271 l 3916 3133 l S NP 3589 3322 m 3709 3391 l 3589 3460 l 3589 3322 l S NP 3916 3271 m 3847 3391 l 3778 3271 l 3916 3271 l S NP 3709 3391 m 3778 3271 l 3847 3391 l 3709 3391 l S NP 3778 3133 m 3916 3133 l 3916 3271 l 3778 3271 l 3778 3133 l S NP 3778 3271 m 3709 3391 l 3589 3322 l 3658 3202 l 3778 3271 l S NP 3847 2499 m 3916 2379 l 3985 2499 l 3847 2499 l 3985 2499 l 3916 2618 l 3847 2499 l S NP 4104 2430 m 3985 2499 l 3916 2379 l 4035 2310 l 4104 2430 l S NP 4035 2687 m 3916 2618 l 3985 2499 l 4104 2568 l 4035 2687 l S NP 3985 2499 m 4104 2430 l 4104 2568 l 3985 2499 l S NP 4035 2310 m 4173 2310 l 4104 2430 l 4035 2310 l S NP 4035 2687 m 4104 2568 l 4173 2687 l 4035 2687 l S NP 4224 2499 m 4104 2568 l 4104 2430 l 4224 2499 l S NP 4173 2310 m 4293 2241 l 4293 2379 l 4173 2310 l S NP 4173 2687 m 4293 2618 l 4293 2756 l 4173 2687 l S NP 4293 2379 m 4362 2499 l 4224 2499 l 4293 2379 l S NP 4293 2618 m 4224 2499 l 4362 2499 l 4293 2618 l S NP 4104 2430 m 4173 2310 l 4293 2379 l 4224 2499 l 4104 2430 l S NP 4224 2499 m 4293 2618 l 4173 2687 l 4104 2568 l 4224 2499 l S NP 4739 2499 m 4670 2618 l 4601 2499 l 4739 2499 l 4601 2499 l 4670 2379 l 4739 2499 l S NP 4481 2568 m 4601 2499 l 4670 2618 l 4550 2687 l 4481 2568 l S NP 4550 2310 m 4670 2379 l 4601 2499 l 4481 2430 l 4550 2310 l S NP 4601 2499 m 4481 2568 l 4481 2430 l 4601 2499 l S NP 4550 2687 m 4412 2687 l 4481 2568 l 4550 2687 l S NP 4550 2310 m 4481 2430 l 4412 2310 l 4550 2310 l S NP 4362 2499 m 4481 2430 l 4481 2568 l 4362 2499 l S NP 4412 2687 m 4293 2756 l 4293 2618 l 4412 2687 l S NP 4412 2310 m 4293 2379 l 4293 2241 l 4412 2310 l S NP 4293 2618 m 4224 2499 l 4362 2499 l 4293 2618 l S NP 4293 2379 m 4362 2499 l 4224 2499 l 4293 2379 l S NP 4481 2568 m 4412 2687 l 4293 2618 l 4362 2499 l 4481 2568 l S NP 4362 2499 m 4293 2379 l 4412 2310 l 4481 2430 l 4362 2499 l S NP 4035 3717 m 3897 3717 l 3966 3598 l 4035 3717 l 3966 3598 l 4104 3598 l 4035 3717 l S NP 3847 3529 m 3966 3598 l 3897 3717 l 3778 3648 l 3847 3529 l S NP 4104 3460 m 4104 3598 l 3966 3598 l 3966 3460 l 4104 3460 l S NP 3966 3598 m 3847 3529 l 3966 3460 l 3966 3598 l S NP 3778 3648 m 3709 3529 l 3847 3529 l 3778 3648 l S NP 4104 3460 m 3966 3460 l 4035 3340 l 4104 3460 l S NP 3847 3391 m 3966 3460 l 3847 3529 l 3847 3391 l S NP 3709 3529 m 3589 3460 l 3709 3391 l 3709 3529 l S NP 4035 3340 m 3916 3271 l 4035 3202 l 4035 3340 l S NP 3709 3391 m 3778 3271 l 3847 3391 l 3709 3391 l S NP 3916 3271 m 3847 3391 l 3778 3271 l 3916 3271 l S NP 3847 3529 m 3709 3529 l 3709 3391 l 3847 3391 l 3847 3529 l S NP 3847 3391 m 3916 3271 l 4035 3340 l 3966 3460 l 3847 3391 l S NP 4739 2499 m 4877 2499 l 4808 2618 l 4739 2499 l S NP 4928 2687 m 4808 2618 l 4877 2499 l 4997 2568 l 4928 2687 l S NP 4808 2618 m 4928 2687 l 4808 2756 l 4808 2618 l S NP 4877 2499 m 4997 2430 l 4997 2568 l 4877 2499 l S NP 5116 2499 m 4997 2568 l 4997 2430 l 5116 2499 l S NP 4928 2825 m 4808 2756 l 4928 2687 l 4928 2825 l S NP 5116 2499 m 5254 2499 l 5185 2618 l 5116 2499 l S NP 4928 2825 m 5066 2825 l 4997 2945 l 4928 2825 l S NP 5066 2687 m 4928 2687 l 4997 2568 l 5066 2687 l S NP 4997 2568 m 5116 2499 l 5185 2618 l 5066 2687 l 4997 2568 l S NP 5066 2687 m 5066 2825 l 4928 2825 l 4928 2687 l 5066 2687 l S NP 5185 2618 m 5185 2756 l 5066 2687 l 5185 2618 l S NP 5066 2825 m 5066 2687 l 5185 2756 l 5066 2825 l S NP 4035 3717 m 4173 3717 l 4104 3837 l 4035 3717 l S NP 4224 3906 m 4104 3837 l 4173 3717 l 4293 3786 l 4224 3906 l S NP 4104 3837 m 4224 3906 l 4104 3975 l 4104 3837 l S NP 4173 3717 m 4293 3648 l 4293 3786 l 4173 3717 l S NP 4412 3717 m 4293 3786 l 4293 3648 l 4412 3717 l S NP 4224 4044 m 4104 3975 l 4224 3906 l 4224 4044 l S NP 4412 3717 m 4550 3717 l 4481 3837 l 4412 3717 l S NP 4224 4044 m 4362 4044 l 4293 4164 l 4224 4044 l S NP 4362 3906 m 4224 3906 l 4293 3786 l 4362 3906 l S NP 4293 3786 m 4412 3717 l 4481 3837 l 4362 3906 l 4293 3786 l S NP 4362 3906 m 4362 4044 l 4224 4044 l 4224 3906 l 4362 3906 l S NP 4481 3837 m 4481 3975 l 4362 3906 l 4481 3837 l S NP 4362 4044 m 4362 3906 l 4481 3975 l 4362 4044 l S NP 4550 3202 m 4431 3271 l 4431 3133 l 4550 3202 l 4431 3133 l 4550 3064 l 4550 3202 l S NP 4293 3133 m 4431 3133 l 4431 3271 l 4293 3271 l 4293 3133 l S NP 4481 2945 m 4550 3064 l 4431 3133 l 4362 3014 l 4481 2945 l S NP 4431 3133 m 4293 3133 l 4362 3014 l 4431 3133 l S NP 4293 3271 m 4155 3271 l 4155 3133 l 4293 3133 l 4293 3271 l S NP 4362 3014 m 4293 2894 l 4412 2825 l 4481 2945 l 4362 3014 l S NP 4155 3133 m 4224 3014 l 4293 3133 l 4155 3133 l S NP 4293 2894 m 4362 3014 l 4224 3014 l 4293 2894 l S NP 4293 3133 m 4224 3014 l 4362 3014 l 4293 3133 l S NP 4035 3202 m 4035 3064 l 4155 3133 l 4035 3202 l S NP 4293 2756 m 4293 2894 l 4173 2825 l 4293 2756 l S NP 4224 3014 m 4155 3133 l 4035 3064 l 4104 2945 l 4224 3014 l S NP 4104 2945 m 4173 2825 l 4293 2894 l 4224 3014 l 4104 2945 l S NP 4035 3202 m 4155 3133 l 4155 3271 l 4035 3202 l S NP 4293 2756 m 4412 2825 l 4293 2894 l 4293 2756 l 4412 2825 l 4293 2894 l 4293 2756 l S NP 4362 3014 m 4293 2894 l 4412 2825 l 4481 2945 l 4362 3014 l S NP 4481 2945 m 4550 3064 l 4431 3133 l 4362 3014 l 4481 2945 l S NP 4550 3202 m 4431 3133 l 4550 3064 l 4550 3202 l S NP 4293 2756 m 4412 2687 l 4412 2825 l 4293 2756 l S NP 4550 3202 m 4550 3064 l 4670 3133 l 4550 3202 l S NP 4859 2945 m 4739 3014 l 4739 2876 l 4859 2945 l S NP 4739 3014 m 4859 2945 l 4928 3064 l 4808 3133 l 4739 3014 l S NP 4601 2499 m 4739 2499 l 4670 2618 l 4601 2499 l S NP 4739 2499 m 4808 2618 l 4670 2618 l 4739 2499 l S NP 4550 2825 m 4412 2825 l 4412 2687 l 4550 2687 l 4550 2825 l S NP 4412 2825 m 4550 2825 l 4481 2945 l 4412 2825 l S NP 4481 2945 m 4550 2825 l 4619 2945 l 4481 2945 l S NP 4550 3064 m 4481 2945 l 4619 2945 l 4550 3064 l S NP 4739 3014 m 4670 3133 l 4550 3064 l 4619 2945 l 4739 3014 l S NP 4412 2687 m 4481 2568 l 4550 2687 l 4412 2687 l S NP 4670 2756 m 4670 2618 l 4808 2618 l 4808 2756 l 4670 2756 l 4808 2756 l 4739 2876 l 4670 2756 l S NP 4808 2756 m 4928 2825 l 4859 2945 l 4739 2876 l 4808 2756 l S NP 4997 2945 m 4859 2945 l 4928 2825 l 4997 2945 l S NP 4670 3133 m 4739 3014 l 4808 3133 l 4670 3133 l S NP 4550 2825 m 4550 2687 l 4670 2756 l 4550 2825 l S NP 4619 2945 m 4739 2876 l 4739 3014 l 4619 2945 l S NP 4739 2876 m 4619 2945 l 4550 2825 l 4670 2756 l 4739 2876 l S NP 4481 2568 m 4601 2499 l 4670 2618 l 4550 2687 l 4481 2568 l S NP 4670 2618 m 4670 2756 l 4550 2687 l 4670 2618 l S NP 4997 2945 m 4928 3064 l 4859 2945 l 4997 2945 l S NP 4808 2618 m 4928 2687 l 4808 2756 l 4808 2618 l S NP 4928 2825 m 4808 2756 l 4928 2687 l 4928 2825 l S NP 4550 3202 m 4431 3271 l 4431 3133 l 4550 3202 l S NP 4293 3133 m 4431 3133 l 4431 3271 l 4293 3271 l 4293 3133 l S NP 4293 3271 m 4155 3271 l 4155 3133 l 4293 3133 l 4293 3271 l S NP 4035 3202 m 4155 3133 l 4155 3271 l 4035 3202 l S NP 4550 3202 m 4550 3340 l 4431 3271 l 4550 3202 l S NP 4035 3202 m 4155 3271 l 4035 3340 l 4035 3202 l S NP 4104 3598 m 4104 3460 l 4224 3529 l 4104 3598 l S NP 4104 3460 m 4104 3598 l 3966 3598 l 3966 3460 l 4104 3460 l S NP 4619 3598 m 4550 3717 l 4481 3598 l 4619 3598 l S NP 4550 3717 m 4412 3717 l 4481 3598 l 4550 3717 l S NP 4362 3391 m 4431 3271 l 4550 3340 l 4481 3460 l 4362 3391 l S NP 4431 3271 m 4362 3391 l 4293 3271 l 4431 3271 l S NP 4293 3271 m 4362 3391 l 4224 3391 l 4293 3271 l S NP 4155 3271 m 4293 3271 l 4224 3391 l 4155 3271 l S NP 4104 3460 m 4035 3340 l 4155 3271 l 4224 3391 l 4104 3460 l S NP 4550 3340 m 4619 3460 l 4481 3460 l 4550 3340 l S NP 4362 3529 m 4481 3598 l 4412 3717 l 4293 3648 l 4362 3529 l 4293 3648 l 4224 3529 l 4362 3529 l S NP 4293 3648 m 4173 3717 l 4104 3598 l 4224 3529 l 4293 3648 l S NP 4035 3717 m 4104 3598 l 4173 3717 l 4035 3717 l S NP 4035 3340 m 4104 3460 l 3966 3460 l 4035 3340 l S NP 4362 3391 m 4481 3460 l 4362 3529 l 4362 3391 l S NP 4224 3391 m 4224 3529 l 4104 3460 l 4224 3391 l S NP 4224 3529 m 4224 3391 l 4362 3391 l 4362 3529 l 4224 3529 l S NP 4619 3460 m 4619 3598 l 4481 3598 l 4481 3460 l 4619 3460 l S NP 4481 3598 m 4362 3529 l 4481 3460 l 4481 3598 l S NP 4035 3717 m 3966 3598 l 4104 3598 l 4035 3717 l S NP 4412 3717 m 4293 3786 l 4293 3648 l 4412 3717 l S NP 4173 3717 m 4293 3648 l 4293 3786 l 4173 3717 l S NP 4997 2945 m 5066 3064 l 4928 3064 l 4997 2945 l 4928 3064 l 4859 2945 l 4997 2945 l S NP 4928 3202 m 4928 3064 l 5066 3064 l 5066 3202 l 4928 3202 l S NP 4739 3014 m 4859 2945 l 4928 3064 l 4808 3133 l 4739 3014 l S NP 4928 3064 m 4928 3202 l 4808 3133 l 4928 3064 l S NP 5066 3202 m 4997 3322 l 4928 3202 l 5066 3202 l S NP 4739 3014 m 4808 3133 l 4670 3133 l 4739 3014 l S NP 4808 3271 m 4808 3133 l 4928 3202 l 4808 3271 l S NP 4997 3322 m 4997 3460 l 4877 3391 l 4997 3322 l S NP 4670 3133 m 4670 3271 l 4550 3202 l 4670 3133 l S NP 4877 3391 m 4739 3391 l 4808 3271 l 4877 3391 l S NP 4670 3271 m 4808 3271 l 4739 3391 l 4670 3271 l S NP 4928 3202 m 4997 3322 l 4877 3391 l 4808 3271 l 4928 3202 l S NP 4808 3271 m 4670 3271 l 4670 3133 l 4808 3133 l 4808 3271 l S NP 4550 3717 m 4481 3598 l 4619 3598 l 4550 3717 l 4619 3598 l 4688 3717 l 4550 3717 l S NP 4619 3460 m 4619 3598 l 4481 3598 l 4481 3460 l 4619 3460 l S NP 4808 3648 m 4688 3717 l 4619 3598 l 4739 3529 l 4808 3648 l S NP 4619 3598 m 4619 3460 l 4739 3529 l 4619 3598 l S NP 4481 3460 m 4550 3340 l 4619 3460 l 4481 3460 l S NP 4808 3648 m 4739 3529 l 4877 3529 l 4808 3648 l S NP 4739 3391 m 4739 3529 l 4619 3460 l 4739 3391 l S NP 4550 3340 m 4550 3202 l 4670 3271 l 4550 3340 l S NP 4877 3529 m 4877 3391 l 4997 3460 l 4877 3529 l S NP 4670 3271 m 4808 3271 l 4739 3391 l 4670 3271 l S NP 4877 3391 m 4739 3391 l 4808 3271 l 4877 3391 l S NP 4619 3460 m 4550 3340 l 4670 3271 l 4739 3391 l 4619 3460 l S NP 4739 3391 m 4877 3391 l 4877 3529 l 4739 3529 l 4739 3391 l S boundarythick setlinewidth %%%% The following draws a box around the plot. %%/bd boundarythick 2 idiv def %%[] 0 setdash %%NP bd bd m bd 5000 bd sub l %%6666 bd sub 5000 bd sub l %%6666 bd sub bd l %%bd bd l S showpage grestore end %%Trailer %%EOF %%EndDocument @endspecial 332 3581 a Fo(Figure)32 b(3:)43 b(A)33 b(\014nite)f(patc)m (h)h(of)f(the)h(maximally)c(symmetric)j(tiling)e(from)h(LI[ST].)-24 3872 y Fa(References)25 4091 y Fo([1])49 b(In)m(ternational)h(T)-8 b(ables)52 b(for)f(Crystallograph)m(y)g(\(V)-8 b(olume)50 b(A\),)h(4th)h(edition,)j(ed.)d(T.)g(Hahn,)177 4211 y(Klu)m(w)m(er)33 b(Academic)f(Publishers)h(\(1983\).)25 4415 y([2])49 b(M.)38 b(Baak)m(e)g(and)f(M.)h(Sc)m(hlottmann,)f(\\Geometric)f(asp)s (ects)i(of)f(tilings)e(and)j(equiv)-5 b(alence)37 b(con-)177 4535 y(cepts",)46 b(in:)64 b Fl(Pr)-5 b(o)g(c)g(e)g(e)g(dings)43 b(of)h(the)g(5th)h(International)e(Confer)-5 b(enc)g(e)43 b(on)h(Quasicrystals)p Fo(,)h(eds.)177 4656 y(C.)33 b(Janot)f(and)h(R.) f(Mosseri,)h(W)-8 b(orld)32 b(Scien)m(ti\014c,)h(Singap)s(ore)e (\(1995\))h(15-21.)25 4859 y([3])49 b(M.)35 b(Baak)m(e,)g(J.)g (Hermisson)f(and)g(P)-8 b(.)35 b(Pleasan)m(ts,)h(\\The)f(torus)f (parametrization)e(of)i(quasip)s(eri-)177 4979 y(o)s(dic)e (LI-classes",)h(J.)f(Ph)m(ys.)j Ff(A)i(30)32 b Fo(\(1997\),)g(in)g (press.)1817 5471 y(19)p eop %%Page: 20 20 20 19 bop 25 407 a Fo([4])49 b(K.)44 b(Niizeki,)j(\\A)d (classi\014cation)g(of)g(sp)s(ecial)f(p)s(oin)m(ts)i(of)f (quasilattices)g(in)g(t)m(w)m(o)h(dimensions",)177 527 y(J.)33 b(Ph)m(ys.)h Ff(A22)e Fo(\(1989\))g(4281-4293.)25 731 y([5])49 b(M.)40 b(Sc)m(hlottmann,)h(\\Geometrisc)m(he)f(Eigensc)m (haften)h(quasip)s(erio)s(disc)m(her)e(Strukturen\\,)k(Dis-)177 851 y(sertation,)32 b(Univ.)h(T)s(\177)-51 b(ubingen)31 b(\(1993\).)25 1054 y([6])49 b(M.)43 b(Go)s(da)e(and)h(H.)h(Kub)s(o,)h (\\A)e(family)e(of)i(Fib)s(onacci)e(lattices",)k(J.)e(Ph)m(ys.)i(So)s (c.)f(Japan)f Ff(58)177 1175 y Fo(\(1989\),)31 b(3624-3634.)25 1378 y([7])49 b(M.)26 b(Degli)e(Esp)s(osti)i(and)g(S.)g(Isola,)g (\\Distribution)d(of)j(closed)g(orbits)f(for)g(linear)f(automorphisms) 177 1499 y(of)32 b(tori",)f(Nonlinearit)m(y)g Ff(8)i Fo(\(1995\))e(827-842.)25 1702 y([8])49 b(M.)e(Baak)m(e,)j(M.)d(Sc)m (hlottmann)e(and)i(P)-8 b(.)46 b(D.)g(Jarvis,)k(\\Quasip)s(erio)s(dic) 44 b(tilings)g(with)i(tenfold)177 1822 y(symmetry)37 b(and)g(equiv)-5 b(alence)37 b(with)f(resp)s(ect)i(to)f(lo)s(cal)d (deriv)-5 b(abilit)m(y",)36 b(J.)h(Ph)m(ys.)h Ff(A24)f Fo(\(1991\))177 1943 y(4637-4654.)25 2146 y([9])49 b(P)-8 b(.)33 b(A.)h(B.)f(Pleasan)m(ts,)h(\\Quasicrystals)f(with)g(arbitrary)f (symmetry)i(group",)f(in:)44 b Fl(Pr)-5 b(o)g(c)g(e)g(e)g(dings)177 2267 y(of)35 b(the)g(5th)g(International)f(Confer)-5 b(enc)g(e)34 b(on)h(Quasicrystals)p Fo(,)d(eds.)i(C.)g(Janot)f(and)g (R.)f(Mosseri,)177 2387 y(W)-8 b(orld)32 b(Scien)m(ti\014c,)g(Singap)s (ore)g(\(1995\))f(22-30.)-24 2590 y([10])49 b(P)-8 b(.)37 b(A.)g(B.)h(Pleasan)m(ts,)h(\\Quasicrystallograph)m(y:)51 b(some)37 b(in)m(teresting)f(new)i(patterns",)h(in)d Fl(Ele-)177 2711 y(mentary)f(and)f(analytic)h(the)-5 b(ory)35 b(of)f(numb)-5 b(ers)32 b Fo(\(PWN,)i(W)-8 b(arsa)m(w,)33 b(1984\),)f(pp.)h(439-61.)-24 2914 y([11])49 b(K.)69 b(Niizeki,)78 b(\\Self-similarit)m(y)64 b(in)69 b(t)m(w)m(o)h (dimensions:)117 b(I.)69 b(The)i Fi(n)p Fo(-gonal)c(quasilattice",)177 3034 y(J.)33 b(Ph)m(ys.)h Ff(A22)e Fo(\(1989\))g(193-204.)-24 3238 y([12])49 b(L.)41 b(C.)h(W)-8 b(ashington,)44 b(\\In)m(tro)s (duction)d(to)g(Cyclotomic)f(Fields",)j(Springer,)g(New)g(Y)-8 b(ork,)44 b(2nd)177 3358 y(edition)31 b(\(1997\).)-24 3562 y([13])49 b(R.)32 b(Lidl)f(and)i(G.)f(Pilz,)g(\\Applied)f (Abstract)i(Algebra",)f(Springer,)g(New)i(Y)-8 b(ork)32 b(\(1984\).)-24 3765 y([14])49 b(R.)32 b(Ammann,)f(B.)h(Gr)s(\177)-51 b(un)m(baum)30 b(and)i(G.)g(C.)g(Shephard,)h(\\Ap)s(erio)s(dic)d (Tiles",)i(Discr.)f(Comput.)177 3885 y(Geom.)g Ff(8)i Fo(\(1992\))f(1-25.)-24 4089 y([15])49 b(P)-8 b(.)89 b(Stamp\015i,)102 b(\\A)89 b(Do)s(decagonal)f(Quasip)s(erio)s(dic)f (Lattice)h(in)h(Tw)m(o)h(Dimensions",)177 4209 y(Helv.)33 b(Ph)m(ys.)h(Acta)f Ff(59)f Fo(\(1986\))g(1260-1263.)-24 4413 y([16])49 b(M.)33 b(Sc)m(hlottmann,)f(priv)-5 b(ate)32 b(comm)m(unication)e(\(1991\).)-24 4616 y([17])49 b(F.)32 b(G\177)-49 b(ahler,)32 b(\\Self-A\016ne)g(Quasip)s(erio)s(dic)e (Tilings",)h(preprin)m(t)i(1996.)1817 5471 y(20)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0204100908105--