# Rhombitetraapeirogonal tiling

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

Rhombitetraapeirogonal tiling

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

## Constructions

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

Name Image Rhombitetrahexagonal tiling [∞,4](*∞42) [∞,∞,∞] = [∞,1+,4](*∞222) rr{∞,4} t0,1,2,3{∞,∞,∞}

## 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.