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Search: id:A068600
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| A068600 |
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Number of n-uniform tilings having n different arrangements of polygons about its vertices. |
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+0
3
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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 are comprised of the three regular tessellations (all triangles, squares, or hexagons) plus the eight semiregular tessellations.
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REFERENCES
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This sequence was originally calculated by Otto Krotenheerdt.
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LINKS
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Steven Dutch, Uniform Tilings
Brian L. Galebach, n-Uniform Tilings
Ng Lay Ling, Honours Project - Tilings and Patterns.
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CROSSREFS
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Cf. A068599.
Sequence in context: A100038 A160843 A153368 this_sequence A158235 A158245 A076851
Adjacent sequences: A068597 A068598 A068599 this_sequence A068601 A068602 A068603
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KEYWORD
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nonn
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AUTHOR
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Brian L. Galebach (sequence(AT)ProbabilitySports.com), Mar 28 2002
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