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.

**References**

Berglund, J. ``Is There a -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.

© 1996-9

1999-05-26