Truncated order-8 triangular tiling

Truncated order-8 triangular tiling
Rank	3
Type	Uniform
Space	Hyperbolic
Notation
Bowers style acronym	Totrat
Coxeter diagram	o8x3x ()
Elements
Faces	8N hexagons, 3N octagons
Edges	12N+24N
Vertices	24N
Vertex figure	Isosceles triangle, edge lengths √2+√2, √3, √3
Measures (edge length 1)
Circumradius	$\frac{\sqrt{-8-9\sqrt2}}{2} ≈ 2.27640 i$
Related polytopes
Army	Totrat
Regiment	Totrat
Dual	Octakis octagonal tiling
Abstract & topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[8,3]
Convex	Yes

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

External links

• Klitzing, Richard. "x3x8o".

• Wikipedia Contributors. "Truncated order-8 triangular tiling".