

A068600


Number of nuniform 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
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OFFSET

1,1


COMMENTS

Sequence gives the number of edgetoedge regularpolygon 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 higheruniform tilings having the equivalent number of distinct polygon arrangements.
There are eleven 1uniform 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)


REFERENCES

This sequence was originally calculated by Otto Krotenheerdt.
Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987, page 69.
Krotenheerdt, Otto. "Die homogenen Mosaike nter Ordnung in der euklidischen Ebene," Wiss. Z. MartinLutherUniv. HalleWittenberg. Math.natur. Reihe, 18(1969), 273290; 19 (1970)1938 and 97122.


LINKS

Table of n, a(n) for n=1..37.
Steven Dutch, Uniform Tilings
Brian L. Galebach, nUniform Tilings
Ng Lay Ling, Honours Project  Tilings and Patterns.


CROSSREFS

Cf. A068599.
List of coordination sequences for uniform planar nets: A008458 (the planar net 3.3.3.3.3.3), A008486 (6^3), A008574 (4.4.4.4 and 3.4.6.4), A008576 (4.8.8), A008579 (3.6.3.6), A008706 (3.3.3.4.4), A072154 (4.6.12), A219529 (3.3.4.3.4), A250120(3.3.3.3.6), A250122 (3.12.12).
Sequence in context: A100038 A160843 A153368 * A158235 A158245 A076851
Adjacent sequences: A068597 A068598 A068599 * A068601 A068602 A068603


KEYWORD

nonn


AUTHOR

Brian Galebach, Mar 28 2002


STATUS

approved



