VW  CVM 1.1 
We say that a wallpaper function f is negating with respect to the isometry h when f(hx) = f(x) for all x in R^{2}. In this case, h is called a negating isometry, or an antisymmetry 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 antisymmetries 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 .

