# Order-8 square tiling

Order-8 square tiling Poincaré disk model of the hyperbolic plane
Type Hyperbolic regular tiling
Vertex configuration 48
Schläfli symbol {4,8}
Wythoff symbol 8 | 4 2
Coxeter diagram     Symmetry group [8,4], (*842)
Dual Order-4 octagonal tiling
Properties Vertex-transitive, edge-transitive, face-transitive

In geometry, the order-8 square tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {4,8}.

## Symmetry

This tiling represents a hyperbolic kaleidoscope of 4 mirrors meeting as edges of a square, with eight squares around every vertex; this symmetry by orbifold notation is called (*4444) with 4 order-4 mirror intersections. In Coxeter notation can be represented as [1+,8,8,1+], (*4444 orbifold) removing two of three mirrors (passing through the square center) in the [8,8] symmetry; the *4444 symmetry can be doubled by bisecting the fundamental domain (square) by a mirror, creating *884 symmetry.

This bicolored square tiling shows the even/odd reflective fundamental square domains of this symmetry; this bicolored tiling has a wythoff construction (4,4,4), or {4},    :

## Related polyhedra and tiling

This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (4n).