# Instructor:Wallpaper Symmetry Solutions

Back to Wallpaper Symmetry Exploration

## Geometric Patterns

A. Square lattice; There are 2- and 4-fold rotations. Symmetry Group *p4m*

B. Triangular lattice; There are 3- and 6-fold rotations. Symmetry Group *p6m*

C. Square lattice; There are 2-fold rotations. Reflections. Symmetry Group *pmm*

D. Parallellogram lattice; There are 2-fold rotations. No reflections. No glide-reflections. Symmetry Group *p2*

E. Parallellogram lattice; There are 2-fold rotations. No reflections. Glide reflections. Symmetry Group *pgg*

F. Hexagonal lattice; There are 3- and 6-fold rotations. No reflections and no glide-reflections. Symmetry Group *p6*

(Note: some of these are hard to see. For instance C and D look like they might have 4-fold rotations, but the angles are not 90 degrees and the symmetry is not quite there if you look carefully ...)

## Recognizable Figures

- Sketch #10:
*pgg* - Sketch #13:
*p4g* - Sketch #17:
*pg* - Sketch #30:
*p1* - Sketch #85:
*p3m1*

Please note that these symmetry grouops (and much more information) is recorded in the back of Visions of Symmetry