A268184 Number of n-isohedral edge-to-edge tilings of regular polygons.

3, 13, 29, 70, 140, 267, 559

Offset: 1

Author

Brian Galebach, Jan 28 2016

Keywords

• hard
• more
• nice
• nonn

Comments

An n-isohedral tiling has n transitivity classes (or "orbits") of faces with respect to the symmetry group of the tiling.

Examples

			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.
		

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

Crossrefs

Analogous to the n-uniform edge-to-edge tilings, which has n orbits of vertices, as opposed to faces (A068599).

Extensions

a(7) from Brian Galebach, Dec 23 2016