1,1

Sequence gives the number of edge-to-edge regular-polygon tilings having n topologically distinct vertex types. Allows tilings with two or more vertex types having the same arrangement of surrounding polygons, as long as those vertices are topologically distinct.

There are eleven 1-uniform tilings (also called the "Archimedean" tessellations) which are comprised of the three regular tessellations (all triangles, squares, or hexagons) plus the eight semiregular tessellations.

D. P. Chavey, Periodic tilings and tilings by regular polygons, PhD thesis, Univ of Wisconsin, Madison, 1984 (gives a(3)).

B. Gruenbaum and G. C. Shephard, Tilings and Patterns, an Introduction, Freeman, 1989; Exercise *6 on p. 70. See Sections 2.1 and 2.2.

Steven Dutch, Uniform Tilings

Brian L. Galebach, n-Uniform Tilings

Ng Lay Ling, Honours Project - Tilings and Patterns.

Eric Weisstein's World of Mathematics, Uniform Tessellation

Cf. A068600.

Sequence in context: A058497 A134782 A067969 this_sequence A085187 A061384 A071154

Adjacent sequences: A068596 A068597 A068598 this_sequence A068600 A068601 A068602

hard,nice,nonn

Brian L. Galebach (sequence(AT)ProbabilitySports.com), Mar 28 2002

151 and 332 found by Brian L. Galebach on Apr 30, 2002, 673 on Aug 06, 2003.