VW - CVM 1.1

Negating Isometries

We say that a wallpaper function f is negating with respect to the isometry h when f(hx) = -f(x) for all x in R². In this case, h is called a negating isometry, or an anti-symmetry of f.

If you have experimented with constructing your own wallpaper functions , you have probably run across some examples of negating isometries, as in some cases it actually requires care to prevent their occurrence.

The next section gives an account of how anti-symmetries arose in our work . We then develops recipes for constructing negating wallpaper functions , but the most elegant treatment of this idea occurs in the next section .

A Motivating Example The Algebra of Wallpapers Table of contents Constructing Wallpaper Functions