Snub tetraheptagonal tiling

Snub tetraheptagonal tiling
Snub tetraheptagonal tiling Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	3.3.4.3.7
Schläfli symbol	sr{7,4} or $s\left\{\begin{array}{c}7\\ 4\end{array}\right\}$
Wythoff symbol	| 7 4 2
Coxeter diagram	File:CDel node h.pngFile:CDel node h.pngFile:CDel 4.pngFile:CDel node h.png
Symmetry group	[7,4]+, (742)
Dual	Order-7-4 floret pentagonal tiling
Properties	Vertex-transitive Chiral

In geometry, the snub tetraheptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of sr{7,4}.

Images

Drawn in chiral pairs, with edges missing between black triangles:

File:H2 snub 247a.pngFile:H2 snub 247b.png

Dual tiling

The dual is called an order-7-4 floret pentagonal tiling, defined by face configuration V3.3.4.3.7.

Related polyhedra and tiling

The snub tetraheptagonal tiling is sixth in a series of snub polyhedra and tilings with vertex figure 3.3.4.3.n. Template:Snub4 table

Template:Order 7-4 tiling table

References

• John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 Search this book on . (Chapter 19, The Hyperbolic Archimedean Tessellations)
• "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678. Search this book on

See also

• Square tiling
• Tilings of regular polygons
• List of uniform planar tilings
• List of regular polytopes

External links

• Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
• Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
• Hyperbolic and Spherical Tiling Gallery
• KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
• Hyperbolic Planar Tessellations, Don Hatch

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