Snub_tetrapeirogonal_tiling

Snub tetraapeirogonal tiling

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

Snub tetraapeirogonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	3.3.4.3.∞
Schläfli symbol	sr{∞,4} or $s{\begin{Bmatrix}\infty \\4\end{Bmatrix}}$
Wythoff symbol	\| ∞ 4 2
Coxeter diagram	or
Symmetry group	[∞,4]⁺, (∞42)
Dual	Order-4-infinite floret pentagonal tiling
Properties	Vertex-transitive Chiral

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4n2 symmetry mutations of snub tilings: 3.3.4.3.n v t e
Symmetry 4n2	Spherical		Euclidean	Compact hyperbolic				Paracomp.
Symmetry 4n2	242	342	442	542	642	742	842	∞42
Snub figures
Config.	3.3.4.3.2	3.3.4.3.3	3.3.4.3.4	3.3.4.3.5	3.3.4.3.6	3.3.4.3.7	3.3.4.3.8	3.3.4.3.∞
Gyro figures
Config.	V3.3.4.3.2	V3.3.4.3.3	V3.3.4.3.4	V3.3.4.3.5	V3.3.4.3.6	V3.3.4.3.7	V3.3.4.3.8	V3.3.4.3.∞

Paracompact uniform tilings in [∞,4] family v t e


{∞,4}	t{∞,4}	r{∞,4}	2t{∞,4}=t{4,∞}	2r{∞,4}={4,∞}	rr{∞,4}	tr{∞,4}
Dual figures


V∞⁴	V4.∞.∞	V(4.∞)²	V8.8.∞	V4^∞	V4³.∞	V4.8.∞
Alternations
[1⁺,∞,4] (*44∞)	[∞⁺,4] (∞*2)	[∞,1⁺,4] (*2∞2∞)	[∞,4⁺] (4*∞)	[∞,4,1⁺] (*∞∞2)	[(∞,4,2⁺)] (2*2∞)	[∞,4]⁺ (∞42)
=				=
h{∞,4}	s{∞,4}	hr{∞,4}	s{4,∞}	h{4,∞}	hrr{∞,4}	s{∞,4}

Alternation duals


V(∞.4)⁴	V3.(3.∞)²	V(4.∞.4)²	V3.∞.(3.4)²	V∞^∞	V∞.4⁴	V3.3.4.3.∞

Snub tetraapeirogonal tiling