Anisohedral Tiling

A plane tiling is said to be isohedral if the symmetry group of the tiling acts transitively on the tiles, and n-isohedral if the tiles fall into n orbits under the action of the symmetry group of the tiling. A k-anisohedral tiling is a tiling which permits no n-isohedral tiling with n<k.


The numbers of anisohedral polyominoes with n=8, 9, 10, ... are 1, 9, 44, 108, 222, ... (OEIS A075206), the first few of which are illustrated above (Myers).

See also

Isohedral Tiling

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Berglund, J. "Is There a k-Anisohedral Tile for k>=5?" Amer. Math. Monthly 100, 585-588, 1993.Berglund, J. "Anisohedral Tilings Page."ünbaum, B. and Shephard, G. C. §9.4 in Tilings and Patterns. New York: W. H. Freeman, 1986.Klee, V. and Wagon, S. Old and New Unsolved Problems in Plane Geometry and Number Theory. Washington, DC: Math. Assoc. Amer., 1991.Myers, J. "Polyomino Tiling.", N. J. A. Sequence A075206 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Anisohedral Tiling

Cite this as:

Weisstein, Eric W. "Anisohedral Tiling." From MathWorld--A Wolfram Web Resource.

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