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A068600 Number of n-uniform tilings having n different arrangements of polygons about their vertices. 5
11, 20, 39, 33, 15, 10, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)



Sequence gives the number of edge-to-edge regular-polygon tilings having n topologically distinct vertex types, with each vertex type having a different arrangement of surrounding polygons. Does not allow for tilings with two or more vertex types having the same arrangement of surrounding polygons, even when those vertices are topologically distinct. There are no 8- or higher-uniform tilings having the equivalent number of distinct polygon arrangements.

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. (See A250120. - N. J. A. Sloane, Nov 29 2014)


This sequence was originally calculated by Otto Krotenheerdt.

Branko Gr├╝nbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987, page 69.

Krotenheerdt, Otto. "Die homogenen Mosaike n-ter Ordnung in der euklidischen Ebene," Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg. Math.-natur. Reihe, 18(1969), 273-290; 19 (1970)19-38 and 97-122.


Table of n, a(n) for n=1..37.

Steven Dutch, Uniform Tilings

Brian L. Galebach, n-Uniform Tilings

Ng Lay Ling, Honours Project - Tilings and Patterns.


Cf. A068599.

List of coordination sequences for uniform planar nets: A008458 (the planar net, A008486 (6^3), A008574 ( and, A008576 (4.8.8), A008579 (, A008706 (, A072154 (4.6.12), A219529 (, A250120(, A250122 (3.12.12).

Sequence in context: A100038 A160843 A153368 * A158235 A158245 A076851

Adjacent sequences:  A068597 A068598 A068599 * A068601 A068602 A068603




Brian Galebach, Mar 28 2002



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Last modified December 10 00:54 EST 2019. Contains 329885 sequences. (Running on oeis4.)