Rhombitetrapentagonal tiling

Rhombitetrapentagonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	4.4.5.4
Schläfli symbol	rr{5,4} or $r{\begin{Bmatrix}5\\4\end{Bmatrix}}$
Wythoff symbol	4 \| 5 2
Coxeter diagram	or
Symmetry group	[5,4], (*542)
Dual	Deltoidal tetrapentagonal tiling
Properties	Vertex-transitive

In geometry, the rhombitetrapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t_0,2{4,5}.

Dual tiling

The dual is called the deltoidal tetrapentagonal tiling with face configuration V.4.4.4.5.

Uniform pentagonal/square tilings
Symmetry: [5,4], (*542)							[5,4]⁺, (542)	[5⁺,4], (5*2)	[5,4,1⁺], (*552)


{5,4}	t{5,4}	r{5,4}	2t{5,4}=t{4,5}	2r{5,4}={4,5}	rr{5,4}	tr{5,4}	sr{5,4}	s{5,4}	h{4,5}
Uniform duals


V5⁴	V4.10.10	V4.5.4.5	V5.8.8	V4⁵	V4.4.5.4	V4.8.10	V3.3.4.3.5	V3.3.5.3.5	V5⁵

*n42 symmetry mutation of expanded tilings: n.4.4.4
Symmetry [n,4], (*n42)	Spherical	Euclidean	Compact hyperbolic				Paracomp.
Symmetry [n,4], (*n42)	*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

John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, 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.

Periodic

Pythagorean Rhombille Schwarz triangle Rectangle Domino Uniform tiling & honeycomb Coloring Convex Kisrhombille Wallpaper group Wythoff

Aperiodic

Ammann–Beenker Aperiodic set of prototiles List Einstein problem Socolar–Taylor Gilbert Penrose Pentagonal Pinwheel Quaquaversal Rep-tile & Self-tiling Sphinx Truchet

Other

Anisohedral & Isohedral Architectonic & catoptric Circle Limit III Computer graphics Honeycomb Isotoxal Packing Problems Domino Wang Heesch's Squaring Prototile Conway criterion Girih Regular Division of the Plane Regular grid Substitution Voronoi Voderberg

This article is issued from Wikipedia - version of the 10/26/2014. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.