Octagonal tiling

Octagonal tiling
Rank	3
Type	Regular
Space	Hyperbolic
Notation
Bowers style acronym	Ocat
Coxeter diagram	x8o3o ()
Schläfli symbol	{8,3}
Elements
Faces	3N octagons
Edges	12N
Vertices	8N
Vertex figure	Triangle, edge length √2+√2
Measures (edge length 1)
Circumradius	$\frac{\sqrt{-3-3\sqrt{2}}}{2} ≈ 1.34561 i$
Related polytopes
Army	Ocat
Regiment	Ocat
Dual	Order-8 triangular tiling
Abstract & topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[8,3]
Convex	Yes

The order-3 octagonal tiling, or just octagonal tiling, is a regular tiling of the hyperbolic plane. 3 octagons join at each vertex.

It can be formed by truncating the order-8 square tiling.

Representations

The octagonal tiling has the following Coxeter diagrams:

• x8o3o (main symmetry)
• o8x4x (as truncated order-8 square tiling)
• x4x4x4*a (octagons of three 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. "Ocat".

• Wikipedia Contributors. "Octagonal tiling".