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Anisohedral tiling

A partial tiling of the plane by Heesch's anisohedral tile. There are two symmetry classes of tiles, one containing the blue and green tiles and the other containing the red and yellow tiles. As Heesch proved, this tile cannot tile the plane with only one symmetry class.

In geometry, a shape is said to be anisohedral if it admits a tiling, but no such tiling is isohedral (tile-transitive); that is, in any tiling by that shape there are two tiles that are not equivalent under any symmetry of the tiling. A tiling by an anisohedral tile is referred to as an anisohedral tiling.[1]

  1. ^ Grünbaum, Branko; Shephard, G. C. (1987). Tilings and Patterns. New York: W. H. Freeman and Company. ISBN 0-7167-1193-1.

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