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 $r{\begin{Bmatrix}7\\4\end{Bmatrix}}$
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

*n42 symmetry mutation of expanded tilings: n.4.4.4
Symmetry [n,4], (*n42)	Spherical	Euclidean	Compact hyperbolic				Paracomp.
	*342 [3,4]	*442 [4,4]	*542 [5,4]	*642 [6,4]	*742 [7,4]	*842 [8,4]	*∞42 [∞,4]
Expanded figures
Config.	3.4.4.4	4.4.4.4	5.4.4.4	6.4.4.4	7.4.4.4	8.4.4.4	∞.4.4.4
Rhombic figures config.	V3.4.4.4	V4.4.4.4	V5.4.4.4	V6.4.4.4	V7.4.4.4	V8.4.4.4	V∞.4.4.4

Uniform heptagonal/square tilings
Symmetry: [7,4], (*742)							[7,4]+, (742)	[7+,4], (7*2)	[7,4,1+], (*772)
{7,4}	t{7,4}	r{7,4}	2t{7,4}=t{4,7}	2r{7,4}={4,7}	rr{7,4}	tr{7,4}	sr{7,4}	s{7,4}	h{4,7}
Uniform duals
V74	V4.14.14	V4.7.4.7	V7.8.8	V47	V4.4.7.4	V4.8.14	V3.3.4.3.7	V3.3.7.3.7	V77

References

• John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (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.

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