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 .
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