Snub pentapentagonal tiling

In geometry, the snub pentapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of sr{5,5}, constructed from two regular pentagons and three equilateral triangles around every vertex.

Snub pentapentagonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	3.3.5.3.5
Schläfli symbol	s{5,4} sr{5,5}
Wythoff symbol	\| 5 5 2
Coxeter diagram	or
Symmetry group	[5⁺,4], (5*2) [5,5]⁺, (552)
Dual	Order-5-5 floret pentagonal tiling
Properties	Vertex-transitive

Uniform pentapentagonal tilings v t e
Symmetry: $[5,5], (*552)$							$[5,5] +, (552)$
=	=	=	=	=	=	=	=

Order-5 pentagonal tiling ${5,5}$	Truncated order-5 pentagonal tiling $t{5,5}$	Order-4 pentagonal tiling $r{5,5}$	Truncated order-5 pentagonal tiling $2t{5,5} = t{5,5}$	Order-5 pentagonal tiling $2r{5,5} = {5,5}$	Tetrapentagonal tiling $rr{5,5}$	Truncated order-4 pentagonal tiling $tr{5,5}$	Snub pentapentagonal tiling $sr{5,5}$
Uniform duals


Order-5 pentagonal tiling $V5.5.5.5.5$	$V5.10.10$	Order-5 square tiling $V5.5.5.5$	$V5.10.10$	Order-5 pentagonal tiling $V5.5.5.5.5$	$V4.5.4.5$	$V4.10.10$	$V3.3.5.3.5$

Uniform pentagonal/square tilings v t e
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

4n2 symmetry mutations of snub tilings: 3.3.n.3.n
Symmetry 4n2	Spherical		Euclidean	Compact hyperbolic				Paracompact
Symmetry 4n2	222	322	442	552	662	772	882	∞∞2
Snub figures
Config.	3.3.2.3.2	3.3.3.3.3	3.3.4.3.4	3.3.5.3.5	3.3.6.3.6	3.3.7.3.7	3.3.8.3.8	3.3.∞.3.∞
Gyro figures
Config.	V3.3.2.3.2	V3.3.3.3.3	V3.3.4.3.4	V3.3.5.3.5	V3.3.6.3.6	V3.3.7.3.7	V3.3.8.3.8	V3.3.∞.3.∞

Snub pentapentagonal tiling

Images

Symmetry

Related tilings

See also

References

External links

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