Truncated octagonal tiling

Truncated octagonal tiling
Rank	3
Type	Uniform
Space	Hyperbolic
Notation
Bowers style acronym	Tocat
Coxeter diagram	x8x3o ()
Elements
Faces	8N triangles, 3N hexadecagons
Edges	12N+24N
Vertices	24N
Vertex figure	Isosceles triangle, edge legnths 1, √2+√2+√2, √2+√2+√2
Measures (edge length 1)
Circumradius	$\frac{\sqrt{-7-7\sqrt2-\sqrt{2+\sqrt2}-\sqrt{4+2\sqrt2}}}{2} ≈ 2.94716 i$
Related polytopes
Army	Tocat
Regiment	Tocat
Dual	Triakis order-8 triangular tiling
Abstract & topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[8,3]
Convex	Yes

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

External links

• Klitzing, Richard. "o3x8x".

• Wikipedia Contributors. "Truncated octagonal tiling".