Snub apeiroapeirogonal tiling

Snub apeiroapeirogonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex figure3.3.∞.3.∞
Schläfli symbolsr{∞,∞}
Wythoff symbol| ∞ ∞ 2
Coxeter diagram
Symmetry group[∞,∞]+, (∞∞2)
DualInfinitely-infinite-order floret pentagonal tiling
PropertiesVertex-transitive Chiral

In geometry, the snub apeiroapeirogonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of s{∞,∞}. It has 3 equilateral triangles and 2 apeirogons around every vertex, with vertex figure 3.3.∞.3.∞.

Dual tiling

Related polyhedra and tiling

Paracompact hyperbolic uniform tilings in [∞,∞] family
Symmetry: [∞,∞], (*∞∞2)

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{∞,∞} t{∞,∞} r{∞,∞} 2t{∞,∞}=t{∞,∞} 2r{∞,∞}={∞,∞} rr{∞,∞} tr{∞,∞}
Dual tilings
V∞∞ V∞.∞.∞ V(∞.∞)2 V∞.∞.∞ V∞∞ V4.∞.4.∞ V4.4.∞
Alternations
[1+,∞,∞]
(*∞∞2)		 [∞+,∞]
(∞*∞)		 [∞,1+,∞]
(*∞∞∞∞)		 [∞,∞+]
(∞*∞)		 [∞,∞,1+]
(*∞∞2)		 [(∞,∞,2+)]
(2*∞∞)		 [∞,∞]+
(2∞∞)
h{∞,∞} s{∞,∞} hr{∞,∞} s{∞,∞} h2{∞,∞} hrr{∞,∞} sr{∞,∞}
Alternation duals
V(∞.∞)∞ V(3.∞)3 V(∞.4)4 V(3.∞)3 V∞∞ V(4.∞.4)2 V3.3.∞.3.∞


See also

Wikimedia Commons has media related to Uniform tiling 3-3-i-3-i.

References

External links