Spacetime Groups

Escher

1. Wallpaper group 2. Chaim colour group regular divisions of the plane

Thumbnails on this index: Eric W. Weisstein, “Wallpaper Groups,” MathWorld; created with Artlandia SymmetryWorks. © Wolfram Research. Labels use Conway orbifold notation. The badge counts Escher’s drawings in that group.

Between 1936 and 1971 M. C. Escher made some 137 numbered regular divisions of the plane — interlocking figures tiling the plane periodically, most of them coloured so that the colouring itself is symmetric. Each drawing is therefore an instance of exactly the two classifications this site catalogues: the wallpaper group of the uncoloured tiling, and the colour group Γ > H of the coloured one. This page files the drawings under both — wallpaper group, then colour group — with the same tabs as Patterns, and with the seat/pattern-type layer removed: a drawing is a picture, not a pattern type.

About the images. Escher’s work is in copyright, and mcescher.com — the site of the rights holder, The M.C. Escher Company B.V. — reserves all rights and asks that nothing be reproduced without written permission. This page therefore reproduces no artwork: every drawing below is a link to the official gallery, and the plate beside each colour group is generated from this site’s own data (data/patterns.json), not from Escher. What is catalogued here are facts — which drawing realises which group — after Doris Schattschneider’s Visions of Symmetry and Caroline MacGillavry’s Symmetry Aspects of M.C. Escher’s Periodic Drawings.

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