Regular and Irregular symmetries of the plane

SIMUW, July 30, 2008

Abstract

Penrose Staircase

I. Regular symmetries: periodic tilings

Four Plane symmetries

Creating wallpaper patterns: FRIES (pgg); GHOSTS (p6)

Problem set

Samples of ALL 17 Wallpaper groups (Crystallographic groups) with names: Birds; Geometric shapes

A short table of characteristics of the symmetry groups

Numbered Escher Symmetry prints

Escher’s symmetry prints from M.C. Escher Official website

Japanese Wallpaper patterns

Alhambra symmetry patterns (controversial issue: are all 17 patterns there?! Check for yourself when you go to Granada)

II. Aperiodic tilings

Hao Wang’s dominos

Kite and Dart

Sun and Star pattern

And a Batman