VW - CVM 1.1

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 .

Informal Discussion of Anti-Symmetries Ways to Visualize Wallpaper Functions Table of contents Negating Isometries