00-255 M. Baake, D. Joseph, and M. Schlottmann

The Root Lattice D_4 and Planar Quasilattices with Octagonal and Dodecagonal Symmetry (1750K, Postscript, gzipped) Jun 5, 00

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Abstract. Quasiperiodic patterns with eight- and twelvefold symmetry are presented which share the root lattice D_4, i.\ e., the 4-D face-centered hypercubic lattice, for their minimal embedding in four-space. We derive the patterns by means of the dualization method and investigate key properties like vertex configurations, local deflation/inflation symmetries and kinematic diffraction. The generalized point symmetries (and thus the Laue group) of these patterns are the dihedral groups d_8 and d_12, respectively, which share a common subgroup, d_4. We introduce a continous one-parameter rotation between the two phases which leaves this subgroup invariant. This should prove useful for modelling alloys like V_15Ni_10Si where quasicrystalline phases with eight- and twelvefold symmetry coexist.

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