|
| |
|
|
A068599
|
|
Number of n-uniform tilings.
|
|
1
| | |
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| 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.
|
|
|
REFERENCES
| 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.
|
|
|
LINKS
| 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
|
|
|
CROSSREFS
| Cf. A068600.
Sequence in context: A058497 A134782 A067969 * A180113 A198310 A085187
Adjacent sequences: A068596 A068597 A068598 * A068600 A068601 A068602
|
|
|
KEYWORD
| hard,nice,nonn
|
|
|
AUTHOR
| Brian L. Galebach (sequence(AT)ProbabilitySports.com), Mar 28 2002
|
|
|
EXTENSIONS
| 151 and 332 found by Brian L. Galebach on Apr 30, 2002, 673 on Aug 06, 2003.
|
| |
|
|
