# Octagonal tiling

Octagonal tiling
Rank3
TypeRegular
SpaceHyperbolic
Notation
Bowers style acronymOcat
Coxeter diagramx8o3o ()
Schläfli symbol{8,3}
Elements
Faces3N octagons
Edges12N
Vertices8N
Vertex figureTriangle, edge length 2+2
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt{-3-3\sqrt{2}}}{2} ≈ 1.34561 i}$
Related polytopes
ArmyOcat
RegimentOcat
DualOrder-8 triangular tiling
Abstract & topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry[8,3]
ConvexYes

The order-3 octagonal tiling, or just octagonal tiling, is a regular tiling of the hyperbolic plane. 3 octagons join at each vertex.

It can be formed by truncating the order-8 square tiling.

## Representations

The octagonal tiling has the following Coxeter diagrams:

## Related polytopes

o8o3o truncations
Name OBSA Schläfli symbol CD diagram Picture
Octagonal tiling ocat {8,3} x8o3o
Truncated octagonal tiling tocat t{8,3} x8x3o
Trioctagonal tiling toct r{8,3} o8x3o
Truncated order-8 triangular tiling totrat t{3,8} o8x3x
Order-8 triangular tiling otrat {3,8} o8o3x
Small rhombitrioctagonal tiling srotoct rr{8,3} x8o3x
Great rhombitrioctagonal tiling grotoct tr{8,3} x8x3x
Snub trioctagonal tiling snatoct sr{8,3} s8s3s