login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A068599 Number of n-uniform tilings. 3
11, 20, 61, 151, 332, 673 (list; graph; refs; listen; history; text; internal format)
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 comprise the three regular tessellations (all triangles, squares, or hexagons) plus the eight semiregular tessellations.

REFERENCES

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.

LINKS

Table of n, a(n) for n=1..6.

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 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,more,nonn

AUTHOR

Brian Galebach, Mar 28 2002

EXTENSIONS

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified October 21 00:56 EDT 2017. Contains 293679 sequences.