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Trihexagonal tiling
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Wikipedia
In geometry, the trihexagonal tiling is a semiregular tiling of the Euclidean plane. There are two triangles and two hexagons alternating on each vertex. It has Schläfli symbol of t1{6,3}.
Conway calls it a hexadeltille.
There are 3 regular and 8 semiregular tilings in the plane.
There are two distinct uniform colorings of a trihexagonal tiling. (Naming the colors by indices on the 4 faces around a vertex (3.6.3.6): 1212, 1232.)
Related polyhedra and tilings
This tiling is topologically related as a part of sequence of rectified polyhedra with vertex figure (3.n.3.n). In this sequence, the edges project into great circles of a sphere on the polyhedra and infinite lines in the planar tiling.
(3.3.3.3) | (3.4.3.4) | (3.5.3.5) |
(3.6.3.6) | (3.7.3.7) | (3.8.3.8) |
And 3-colors with even orders: 3.2n.3.2n:
(3.4.3.4) | (3.6.3.6) | (3.8.3.8) |
See also
References
- Grünbaum, Branko ; and Shephard, G. C. (1987). Tilings and Patterns. New York: W. H. Freeman. ISBN 0-716-71193-1. (Chapter 2.1: Regular and uniform tilings, p.58-65)
- Williams, Robert The Geometrical Foundation of Natural Structure: A Source Book of Design New York: Dover, 1979. p38
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Last updated on Wednesday June 04, 2008 at 16:49:45 PDT (GMT -0700)
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This article is licensed under the GNU Free Documentation License.
Last updated on Wednesday June 04, 2008 at 16:49:45 PDT (GMT -0700)
View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation
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