Rhombitetraapeirogonal tiling

Rhombitetraapeirogonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex configuration4.4..4
Schläfli symbolrr{,4}
Wythoff symbol4 | 2
Coxeter diagram
Symmetry group[,4], (*42)
DualDeltoidal tetraapeirogonal tiling
PropertiesVertex-transitive

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

Constructions

There are two uniform constructions of this tiling, one from [∞,4] or (*∞42) symmetry, and secondly removing the miror middle, [∞,1+,4], gives a rectangular fundamental domain [∞,∞,∞], (*∞222).

Two uniform constructions of 4.4.4.∞
Name Rhombitetrahexagonal tiling
Image
Symmetry [∞,4]
(*42)
[∞,∞,∞] = [∞,1+,4]
(*222)
Schläfli symbol rr{∞,4} t0,1,2,3{∞,∞,∞}
Coxeter diagram

Symmetry

The dual of this tiling, called a deltoidal tetraapeirogonal tiling represents the fundamental domains of (*∞222) orbifold symmetry. Its fundamental domain is a Lambert quadrilateral, with 3 right angles.

Related polyhedra and tiling

See also

Wikimedia Commons has media related to Uniform tiling 4-4-4-i.

References

External links

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