Triheptagonal tiling

In geometry, the triheptagonal tiling is a semiregular tiling of the hyperbolic plane. There are two triangles and two heptagons alternating on each vertex. It has Schläfli symbol of "t₁{7,3}".

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

Compare to Trihexagonal tiling with vertex configuration "3.6.3.6".

Dual tiling

The dual tiling is called an "Order-7-3 quasiregular rhombic tiling", made from rhombic faces, alternating 3 and 7 per vertex.:

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

* Trihexagonal tiling - 3.6.3.6 tiling
** Quasiregular rhombic tiling - dual V3.6.3.6 tiling
* Tilings of regular polygons
* List of uniform 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]