Snub tetraapeirogonal tiling

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

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

Images

Drawn in chiral pairs, with edges missing between black triangles:

Related polyhedra and tiling

The snub tetrapeirogonal tiling is last in an infinite series of snub polyhedra and tilings with vertex figure 3.3.4.3.n.

4n2 symmetry mutations of snub tilings: 3.3.4.3.n

Symmetry 4n2	Spherical		Euclidean	Compact hyperbolic				Paracomp.
	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
{∞,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^∞	V4^3.∞	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∞.4^4	V3.3.4.3.∞

See also

• Square tiling
• Tilings of regular polygons
• List of uniform planar tilings
• List of regular polytopes

References

• 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.

External links

• Weisstein, Eric W., "Hyperbolic tiling", MathWorld.
• Weisstein, Eric W., "Poincaré hyperbolic disk", MathWorld.
• Hyperbolic and Spherical Tiling Gallery