Two-Dimensional Groups, Orbifolds and Tilings

Ludwig Balke and Daniel H. Huson

Abstract:
Given the triangulation of a 2-dimensional orbifold in
terms of the Delaney--Dress symbol of a periodic tiling, we
discuss how to compute it's orbifold symbol, as defined by J.~Conway.
It is shown that the number of types of equivariant tilings depends only on
the ``form'' of the corresponding orbifold symbols.
The method is applied to obtain a refined classification of equivariant
tilings for certain hyperbolic symmetry groups.

Appeared in:
Geometriae Dedicata, 60:89--106, 1996