Michael Baake, Joachim Hermisson, Peter A.B. Pleasants
The torus parametrization of quasiperiodic LI-classes
(720K, Postscript)

ABSTRACT.  The torus parametrization of quasiperiodic local isomorphism classes is 
introduced and used to determine the number of elements in such a class 
with special symmetries or inflation properties. The method is explained 
in an illustrative fashion for some widely used tiling classes with 
golden mean rescaling, namely for the Fibonacci chain (1D), the triangle 
and Penrose patterns (2D) and for Kramer's and Danzer's icosahedral 
tilings (3D). We obtain a rather complete picture of the orbit structure 
within these classes, but discuss also various general results.