# Octagonal tiling

Octagonal tiling Poincaré disk model of the hyperbolic plane
Type Hyperbolic regular tiling
Vertex configuration 83
Schläfli symbol {8,3}
t{4,8}
Wythoff symbol 3 | 8 2
2 8 | 4
4 4 4 |
Coxeter diagram              Symmetry group [8,3], (*832)
[8,4], (*842)
[(4,4,4)], (*444)
Dual Order-8 triangular tiling
Properties Vertex-transitive, edge-transitive, face-transitive

In geometry, the octagonal tiling is a regular tiling of the hyperbolic plane. It is represented by Schläfli symbol of {8,3}, having three regular octagons around each vertex. It also has a construction as a truncated order-8 square tiling, t{4,8}.

## Uniform colorings

Like the hexagonal tiling of the Euclidean plane, there are 3 uniform colorings of this hyperbolic tiling. The dual tiling V8.8.8 represents the fundamental domains of [(4,4,4)] symmetry.

Regular Truncations

{8,3}

t{4,8}

t{4}
=       =
Dual tiling

{3,8}
=

=

=       =

## Related polyhedra and tilings

This tiling is topologically part of sequence of regular polyhedra and tilings with Schläfli symbol {n,3}.

And also is topologically part of sequence of regular tilings with Schläfli symbol {8,n}.

From a Wythoff construction there are ten hyperbolic uniform tilings that can be based from the regular octagonal tiling.

Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 10 forms.