Let 
be the group of symmetries which map a monohedral
tiling 
onto itself. The transitivity class of a given
tile T is then the collection of all tiles to which T can be mapped by one of the
symmetries of 
.
If 
has 
transitivity classes, then 
is said to be 
-isohedral. Berglund (1993) gives examples of 
-isohedral tilings for 
, 2, and 4.
The numbers of isohedral 
-polyomino tilings (more specifically, the number of polyominoes
with 
cells that tile the plane by 
rotation but not by translation) for 
, 8, 9, ... are 3, 11, 60, 199, 748, ... (OEIS A075201),
the first few of which are illustrated above (Myers).
The numbers of 
-polyomino
tilings that tile the plane isohedrally without additional restriction for 
, 2, ... are 1, 1, 2, 5, 12, 35, 104, ... (OEIS A075205).
-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."