Great rhombitriheptagonal tiling

In geometry, the great rhombitrihexagonal tiling (or "omnitruncated trihexagonal tiling") is a semiregular tiling of the Euclidean plane. There are one square, one hexagon, and one tetrakaidecagon(14-sides) on each vertex. It has Schläfli symbol of "t_0,1,2{7,3}".

The image shows a Poincaré disk model projection of the hyperbolic plane.

This tiling is topologically related as a part of sequence of omnitruncated polyhedra with vertex figure (4.6.2n). This set of polyhedra are zonohedrons.

There is only one uniform colorings of an "great rhombitrihexagonal tiling". (Naming the colors by indices around a vertex: 123.)

Dual tiling

The dual tiling is called an "order-3 bisected heptagonal tiling", made as a complete bisection of the order-3 heptagonal tiling, here with triangles colored alternatingly white and blue. :

Each triangle in this dual tiling represent a fundamental domain of the Wythoff construction for the symmetry group [7,3] .

References

*cite book
last=Grünbaum
first=Branko
authorlink=Branko Grünbaum
coauthors=Shephard, G. C.
title=Tilings and Patterns
location=New York
publisher=W. H. Freeman and Company
year=1987
isbn=0-7167-1193-1
#if: {chapter|} |chapter={chapter}
#if: {pages|} |pages={pages}

See also

* Tilings of regular polygons
* List of uniform planar tilings

External links

*MathWorld | urlname= HyperbolicTiling | title = Hyperbolic tiling
*MathWorld | urlname=PoincareHyperbolicDisk | title = Poincaré hyperbolic disk
* [http://bork.hampshire.edu/~bernie/hyper/ Hyperbolic and Spherical Tiling Gallery]
* [http://geometrygames.org/KaleidoTile/index.html KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings]
* [http://www.hadron.org/~hatch/HyperbolicTesselations Hyperbolic Planar Tessellations, Don Hatch]