M. Baake, D. Joseph, and M. Schlottmann
The Root Lattice D_4 and Planar Quasilattices with 
Octagonal and Dodecagonal Symmetry
(1750K, Postscript, gzipped)

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.