Anisohedral Tiling
A plane tiling is said to be isohedral if the symmetry group of the tiling acts transitively on the tiles, and 
-isohedral if the tiles fall into n orbits
under the action of the symmetry group of the tiling. A 
-anisohedral tiling
is a tiling which permits no 
-isohedral
tiling with 
.
The numbers of anisohedral polyominoes with 
, 9, 10, ...
are 1, 9, 44, 108, 222, ... (OEIS A075206),
the first few of which are illustrated above (Myers).
Berglund, J. "Is There a 
-Anisohedral Tile
for 
?" Amer. Math. Monthly 100,
585-588, 1993.
Berglund, J. "Anisohedral Tilings Page." https://www.angelfire.com/mn3/anisohedral/.
Grünbaum, 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." https://www.srcf.ucam.org/~jsm28/tiling/.
Sloane, N. J. A. Sequence A075206 in "The On-Line Encyclopedia of Integer Sequences."
Weisstein, Eric W. "Anisohedral Tiling." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AnisohedralTiling.html
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