Tilings and groups

From: Gerard Westendorp <westy31@xxxxxxxxx>
Date: Tue, 13 Feb 2007 22:15:13 +0100

I was wondering if it is true that every group with 2 generators can be
thought of as tiling of a 2-dimensional surface.

The orbits of both generators in a 2-generator group can
also be thought of as a polygons with the number of sides is equal to the order of the generator. Many well known groups with 2
generators are tilings, such as the symmetry groups of polyhedra.

Intuitively it woulds seem to me that this is always true, but I'm not
sure.

Gerard

.

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  - From: Christopher J. Henrich

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Re: Tilings and groups
... "Can a Platonic tesselation of a 2 dimensional manifold be constructed ... for any groups with 2 generators?" ... Then you can create a planar Cayley graph for this group. ... The Cayley graph is itself an planar Archemedean tiling, ...
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Re: Tilings and groups
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