# Truncated octagonal tiling

Truncated octagonal tiling
Rank3
TypeUniform
SpaceHyperbolic
Notation
Bowers style acronymTocat
Coxeter diagramx8x3o ()
Elements
Edges12N+24N
Vertices24N
Vertex figureIsosceles triangle, edge legnths 1, 2+2+2, 2+2+2
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt{-7-7\sqrt2-\sqrt{2+\sqrt2}-\sqrt{4+2\sqrt2}}}{2} ≈ 2.94716 i}$
Related polytopes
ArmyTocat
RegimentTocat
DualTriakis order-8 triangular tiling
Abstract & topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry[8,3]
ConvexYes

The truncated octagonal tiling or tocat is a uniform tiling of the hyperbolic plane. 2 hexadecagons and 1 triangle join at each vertex. It can be formed from the truncation of the octagonal tiling.

## 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