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