An anisohedral tiling uses a tile shape that tiles the plane but admits no isohedral tiling . For a positive
integer tiling is orbits under its symmetry
group . For an integer tiling and no tiling with
The numbers of anisohedral polyominoes , counted up to congruence including reflection ,
with A075206 ),
the first few of which are illustrated above (Myers 2026).
See also Isohedral Tiling
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References Berglund, J. "Is There a Amer. Math. Monthly 100 , 585-588,
1993. Berglund, J. "Anisohedral Tilings Page." https://johndberglund.github.io/anisohedral/index.html . Grünbaum,
B. and Shephard, G. C. §9.4 in Tilings
and Patterns. Klee,
V. and Wagon, S. Old
and New Unsolved Problems in Plane Geometry and Number Theory. Myers, J. "Polyform Tiling."
Jul. 17, 2026. https://www.polyomino.org.uk/mathematics/polyform-tiling/ . Sloane,
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 https://mathworld.wolfram.com/AnisohedralTiling.html
Subject classifications
,
a tiling is 
-isohedral if its tiles form exactly 
orbits under its symmetry
group. For an integer 
, a tile shape is 
-anisohedral if it admits a 
-isohedral tiling and no 
-isohedral tiling with 
.
,
9, 10, ... are 1, 9, 44, 108, 222, ... (OEIS A075206),
the first few of which are illustrated above (Myers 2026).
-Anisohedral Tile for 
?" Amer. Math. Monthly 100, 585-588,
1993.Berglund, J. "Anisohedral Tilings Page."