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 .
See also Monohedral Tiling
Berglund, J. ``Is There a -Anisohedral Tile for ?'' Amer. Math. Monthly 100, 585-588, 1993.