Two-dimensional groups, orbifolds and tilings

✍ Scribed by Ludwig Balke; Daniel H. Huson

• Book ID: 104643563
• Publisher: Springer
• Year: 1996
• Tongue: English
• Weight: 873 KB
• Volume: 60
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00150869

✦ Synopsis

Given the triangulation of a 2-dimensional orbifold in terms of the Delaney-Dress symbol of a periodic tiling, we discuss how to compute its 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.