|VW - CVM 1.1|
For example, consider the cell diagram for the group pgg below.
|The pgg cell.|
The group pgg is generated by the half-turn
RC and the horizontal glide
B labeled in the diagram. You can't have these two symmetries
without having Bv as well. This is because
Bv is the result of performing B and then
RC in succession. That is,
A wallpaper group must contain translations in two independent directions ; why aren't any translations listed among the generators? It's because the they can be expressed as B2 and Bv2. Hence all the isometries in the group pgg can be expressed as compositions of the two transformations B and RC.