Order-8 triangular tiling

Order-8 triangular tiling
Rank	3
Type	Regular
Space	Hyperbolic
Notation
Bowers style acronym	Otrat
Coxeter diagram	o8o3x ()
Schläfli symbol	{3,8}
Elements
Faces	8N triangles
Edges	12N
Vertices	3N
Vertex figure	Octagon, edge length 1
Measures (edge length 1)
Circumradius	$\frac{i\sqrt[4]{2}}{2} ≈ 0.59460 i$
Related polytopes
Army	Otrat
Regiment	Otrat
Dual	Octagonal tiling
Topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[8,3]
Convex	Yes

The order-8 triangular tiling is a regular tiling of the hyperbolic plane. 8 triangles join at each vertex.

Representations

An order-8 triangular tiling has the following Coxeter diagrams:

• o8o3x (full symmetry)
• o3x3o4*a (triangles of two alternating types)

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. "Otrat".

• Wikipedia Contributors. "Order-8 triangular tiling".