Rhombitetraapeirogonal tiling

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 mirror middle, [∞,1+,4], gives a rectangular fundamental domain [∞,∞,∞], (*∞222).

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.
 * H2chess 24id.pngDeltoidal tetraapeirogonal tiling.png