An isohedral tiling is a monohedral tiling whose symmetry group has a transitive
group action on its tiles. Let 
be the symmetry group
of a tiling 
. The transitivity class
of a tile 
consists of all tiles to which 
can be mapped by an element of
. If 
has 
such transitivity classes,
then 
is 
-isohedral.
Thus an isohedral tiling is 1-isohedral. Berglund (1993) gives examples of 
-isohedral tilings for 
, 2, and 4.
The numbers of polyominoes with 
cells that admit a tiling of the
plane by 
rotation but not by translation
are 3, 11, 60, 199, 748, ... for 
, 6, 7, ... (OEIS A075201).
Examples are illustrated above (Myers).
The numbers of polyominoes with 
cells that admit an isohedral tiling without additional restriction
are 1, 1, 2, 5, 12, 35, 104, ... for 
, 2, ... (OEIS A075205).
These counts identify polyominoes related by rotation
or reflection (Myers).
-Anisohedral Tile for 
?" Amer. Math. Monthly 100, 585-588,
1993.Grünbaum, B. and Shephard, G. C. "The 81 Types of
Isohedral Tilings of the Plane." Math. Proc. Cambridge Philos. Soc. 82,
177-196, 1977.Keating, K. and Vince, A. "Isohedral Polyomino Tiling
of the Plane." Disc. Comput. Geom. 21, 615-630, 1999.Myers,
J. "Polyomino Tiling."