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