Symmetries of the plane: what group theory tells us about tilings in Escher prints?

SIMUW, July 17, 2019

Abstract

Penrose Staircase and an animated one

I. Regular symmetries: periodic tilings

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

More symmetry prints

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

Alhambra symmetry patterns (controversial issue: are all 17 patterns there?! Check for yourself when you go to Granada. Or check out these two papers: Branko Grunbaum; R. Perez-Gomez.)

II. Aperiodic tilings

Hao Wang’s dominos

Kite and Dart and on wikipedia

Sun and Star pattern

Movie about Penrose tiles: Part 1 and Part 2

And a Batman