Small rhombitrioctagonal tiling

Small rhombitrioctagonal tiling
Rank	3
Type	Uniform
Space	Hyperbolic
Notation
Bowers style acronym	Srotoct
Coxeter diagram	x8o3x ()
Elements
Faces	8N triangles, 12N squares, 3N octagons
Edges	24N+24N
Vertices	24N
Vertex figure	Isosceles trapezoid, edge legnths 1, √2, √2+√2, √2
Measures (edge length 1)
Circumradius	$\frac{\sqrt{-3-4\sqrt2-2\sqrt{2+\sqrt2}-2\sqrt{4+2\sqrt2}}}{2} ≈ 2.09634 i$
Related polytopes
Army	Srotoct
Regiment	Srotoct
Dual	Deltoidal trioctagonal tiling
Abstract & topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[8,3]
Convex	Yes

The small rhombitrioctagonal tiling, or simply rhombitrioctagonal tiling, is a uniform tiling of the hyperbolic plane. 1 octagon, 1 triangle, and 2 squares join at each vertex. It can be formed by cantellation of either the octagonal tiling or its dual order-8 triangular tiling, or equivalently by rectification of the trioctagonal 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. "srotoct".

• Wikipedia Contributors. "Rhombitrioctagonal tiling".