Tetraoctagonal tiling


In geometry, the tetraoctagonal tiling is a uniform tiling of the hyperbolic plane.

Constructions

There are for uniform constructions of this tiling, three of them as constructed by mirror removal from the or orbifold symmetry. Removing the mirror between the order 2 and 4 points,, gives,. Removing the mirror between the order 2 and 8 points,, gives,. Removing both mirrors,, leaves a rectangular fundamental domain,,.
NameTetra-octagonal tilingRhombi-octaoctagonal tiling
Image
Symmetry
 =
= 		=
= 		=
= or
Schläflirrr
=r1/2		r
=r1/2		t0,1,2,3
=r1/4
Coxeter = = = or

Symmetry

The dual tiling has face configuration V4.8.4.8, and represents the fundamental domains of a quadrilateral kaleidoscope, orbifold, shown here. Adding a 2-fold gyration point at the center of each rhombi defines a orbifold.