# Truncated order-8 triangular tiling

Truncated order-8 triangular tiling
Rank3
TypeUniform
SpaceHyperbolic
Notation
Bowers style acronymTotrat
Coxeter diagramo8x3x ()
Elements
Faces8N hexagons, 3N octagons
Edges12N+24N
Vertices24N
Vertex figureIsosceles triangle, edge lengths 2+2, 3, 3
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt{-8-9\sqrt2}}{2} ≈ 2.27640 i}$
Related polytopes
ArmyTotrat
RegimentTotrat
DualOctakis octagonal tiling
Abstract & topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry[8,3]
ConvexYes

The truncated order-8 triangular tiling or totrat is a uniform tiling of the hyperbolic plane. 2 hexagons and 1 octagon join at each vertex. It can be formed from the truncation of the order-8 triangular tiling.

It is also the omnitruncate of the (4,3,3) family of tilings, with Coxeter diagram .

## Representations

A truncated order-8 triangular tiling has the following Coxeter diagrams:

• o8x3x (full symmetry)
• x3x3x4*a (half symmetry)

## 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
o4o3o3*a truncations
Name OBSA CD diagram Picture
Ditrigonary tritetragonal tiling
Order-8 triangular tiling
Trioctagonal tiling
Rectified ditrigonary tritetragonal tiling
Truncated order-8 triangular tiling
Snub tritritetragonal tiling