Talk:Symmetry, Escher and Architecture Exploration
1. The overall facade has a single reflection symmetry, but the pegasus pattern itself does not.
4. Order 2 and 4 rotations. Wallpaper group p4.
5. Only translation. Wallpaper group p1.
6. Vertical glide reflections. Wallpaper group pg.
7. Order 2 rotation. Almost has reflection symmetry and order 4 rotation except both are ruined by the overlap of the white bars. Wallpaper group is p2 but almost p4g. Also, the individual flower motifs have D5 symmetry.
8. No rotations. Vertical glide reflections. Wallpaper group pg.
9. The flower pillar needs two tiles that could be the same if flat. Because it's curved, you need one tile with center bar vertical and one with center bar horizontal. The second pillar needs only one tile but needs two different colorings. One has white birds and black fish, the other has black birds and white fish.