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
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