Rhombitetraheptagonal tiling

Rhombitetraheptagonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	4.4.7.4
Schläfli symbol	rr{7,4} or $r\left\{\begin{array}{c}7\\ 4\end{array}\right\}$
Wythoff symbol	4 | 7 2
Coxeter diagram
Symmetry group	[7,4], (*742)
Dual	Deltoidal tetraheptagonal tiling
Properties	Vertex-transitive

In geometry, the rhombitetraheptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of rr{4,7}. It can be seen as constructed as a rectified tetraheptagonal tiling, r{7,4}, as well as an expanded order-4 heptagonal tiling or expanded order-7 square tiling.

Dual tiling

The dual is called the deltoidal tetraheptagonal tiling with face configuration V.4.4.4.7.

Related polyhedra and tiling

Template:Expanded4 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

• Uniform tilings in hyperbolic plane
• 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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