Snub tetraheptagonal tiling

Snub tetraheptagonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	3.3.4.3.7
Schläfli symbol	sr{7,4} or ${\displaystyle s{\begin{Bmatrix}7\\4\end{Bmatrix}}}$
Wythoff symbol	| 7 4 2
Coxeter diagram
Symmetry group	[7,4]+, (742)
Dual	Order-7-4 floret pentagonal tiling
Properties	Vertex-transitive Chiral

In geometry, the snub tetraheptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of sr{7,4}.

Images

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

Dual tiling

The dual is called an order-7-4 floret pentagonal tiling, defined by face configuration V3.3.4.3.7.

Related polyhedra and tiling

The snub tetraheptagonal tiling is sixth in a 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 v t e
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.∞

Uniform heptagonal/square tilings v t e
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

Wikimedia Commons has media related to Uniform tiling 3-3-4-3-7.