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The Algebra of Wallpapers

Algebra is the key to classifying the different types of wallpaper functions and proving that we have indeed given a recipe for each possible type. In this classification we must consider two groups: the group G of symmetries enjoyed by the pattern, and a possibly larger group E containing all its anti-symmetries in addition.

We begin with an informal discussion of the concepts used in this section . The reader interested in the technical definitions may proceed to the section on combining negating isometries . The classification result is proved by means of an exhaustive list of all possibilities, with care to identify any two that are equivalent .

[Next] Informal Discussion of Anti-Symmetries
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[Prev] Negating Isometries

Communications in Visual Mathematics, vol 1, no 1, August 1998.
Copyright © 1998, The Mathematical Association of America. All rights reserved.
Created: 08 Jul 1998 --- Last modified: 18 Aug 1998 23:59:59
Comments to: CVM@maa.org