OFFSET
1,1
COMMENTS
An n-isohedral tiling has n transitivity classes (or "orbits") of faces with respect to the symmetry group of the tiling.
LINKS
D. Chavey, Periodic Tilings and Tilings by Regular Polygons I, Thesis, 1984, pp. 165-172 gives the 2-isohedral edge-to-edge tilings of regular polygons.
D. Chavey, Tiling by Regular Polygons II: A Catalog of Tilings, Computers & Mathematics with Applications, Volume 17, Issues 1-3, 1989, Pages 147-165, illustrates 27 of the 29 3-isohedral edge-to-edge tilings of regular polygons, but classifies one (3^3.4^2; 3^2.4.3.4)2 on page 152 as 6-isohedral.
Brian Galebach, Announcement of 7-Isohedral Tiling Count, Facebook
EXAMPLE
The three 1-isohedral tilings are the regular tilings (triangles, squares, hexagons). Of the 13 2-isohedral tilings, there are three with triangles and squares, eight with triangles and hexagons, one with triangles and dodecagons, and one with squares and octagons.
CROSSREFS
KEYWORD
hard,more,nice,nonn
AUTHOR
Brian Galebach, Jan 28 2016
EXTENSIONS
a(7) from Brian Galebach, Dec 23 2016
STATUS
approved