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A068599 Number of n-uniform tilings. 7
11, 20, 61, 151, 332, 673, 1472 (list; graph; refs; listen; history; text; internal format)



Sequence gives the number of edge-to-edge regular-polygon tilings having n vertex classes relative to the symmetry of the tiling. Allows tilings with two or more vertex classes having the same arrangement of surrounding polygons (vertex type), as long as those classes are distinct within the symmetry of the tiling .

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


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


Table of n, a(n) for n=1..7.

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

Steven Dutch, Uniform Tilings

Brian Galebach, n-Uniform Tilings

Brian Galebach, 7-Uniform Tiling Example, shows a tiling with 7 vertex classes (7-uniform), and 6 vertex types (6-Archimedean).

Ng Lay Ling, Honours Project - Tilings and Patterns.

N. J. A. Sloane, Coordination Sequences, Planing Numbers, and Other Recent Sequences (II), Experimental Mathematics Seminar, Rutgers University, Jan 31 2019, Part I, Part 2, Slides. (Mentions this sequence)

Eric Weisstein's World of Mathematics, Uniform Tessellation


Cf. A068600.

Sequence in context: A058497 A134782 A067969 * A180113 A198310 A085187

Adjacent sequences:  A068596 A068597 A068598 * A068600 A068601 A068602




Brian Galebach, Mar 28 2002


151 and 332 found by Brian Galebach on Apr 30 2002, 673 on Aug 06 2003, 1472 on Apr 28 2020



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Last modified June 21 09:45 EDT 2021. Contains 345358 sequences. (Running on oeis4.)