Trioctagonal tiling

Trioctagonal tiling
Rank	3
Type	Uniform
Space	Hyperbolic
Notation
Bowers style acronym	Toct
Coxeter diagram	o8x3o ()
Elements
Faces	8N triangles, 3N octagons
Edges	24N
Vertices	12N
Vertex figure	Rectangle, edge lengths 1 and √2+√2
Measures (edge length 1)
Circumradius	$\sqrt{-1-\sqrt2} ≈ 1.55377 i$
Related polytopes
Army	Toct
Regiment	Toct
Dual	8-3 rhombille tiling
Abstract & topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[8,3]
Convex	Yes

The trioctagonal tiling or toct is a uniform tiling of the hyperbolic plane. 2 octagons and 2 triangles join at each vertex. It can be formed from the rectification of either the octagonal tiling or its dual order-8 triangular tiling.

Representations

A trioctagonal tiling has the following Coxeter diagrams:

• o8x3o (full symmetry)
• x3o3x4*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. "toct".

• Wikipedia Contributors. "Trioctagonal tiling".