Geometry of Surfaces pp 163-183 | Cite as

# Planar and Spherical Tessellations

Chapter

## Abstract

By a *tessellation T* we mean a division of a geometric surface into nonoverlapping congruent polygons, called *tiles. T* is *symmetric* if it “looks the same from the viewpoint of any tile”, i.e., if any tile II_{1} can be mapped onto any tile II_{2} by an isometry which maps the whole of *T* onto itself (faces onto faces and edges onto edges). The isometries of *T* onto itself are called *symmetries* of *T*, and they form a group called the *symmetry group* of *T.* Thus, we are defining *T* to be symmetric if its symmetry group contains enough elements to map any tile onto any other tile.

## Keywords

Symmetry Group Equilateral Triangle Cayley Graph Hyperbolic Surface Angle Condition
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 1992