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anisohedral tiling
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.
==Existence==
The second part of Hilbert's eighteenth problem asked whether there exists an anisohedral polyhedron in Euclidean 3-space; Grünbaum and Shephard suggest〔Grünbaum and Shephard, section 9.6〕 that Hilbert was assuming that no such tile existed in the plane. Reinhardt answered Hilbert's problem in 1928 by finding examples of such polyhedra, and asserted that his proof that no such tiles exist in the plane would appear soon. However, Heesch then gave an example of an anisohedral tile in the plane in 1935.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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