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Snub tetrapentagonal tiling

## Summary

Snub tetrapentagonal tiling

Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 3.3.4.3.5
Schläfli symbol sr{5,4} or ${\displaystyle s{\begin{Bmatrix}5\\4\end{Bmatrix}}}$
Wythoff symbol | 5 4 2
Coxeter diagram or
Symmetry group [5,4]+, (542)
Dual Order-5-4 floret pentagonal tiling
Properties Vertex-transitive Chiral

In geometry, the snub tetrapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of sr{5,4}.

## Images

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

## Dual tiling

The dual is called an order-5-4 floret pentagonal tiling, defined by face configuration V3.3.4.3.5.

## Related polyhedra and tiling

The snub tetrapentagonal tiling is fourth 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
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 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