Great rhombitrioctagonal tiling

Great rhombitrioctagonal tiling
Rank	3
Type	Uniform
Space	Hyperbolic
Notation
Bowers style acronym	Grotoct
Coxeter diagram	x8x3x ()
Elements
Faces	12N squares, 8N hexagons, 3N hexadecagons
Edges	24N+24N+n24N
Vertices	48N
Vertex figure	Scalene triangle, edge lengths √2, √2+√2, √2+√2+√2
Measures (edge length 1)
Circumradius	$\frac{\sqrt{-11-12\sqrt2-6\sqrt{2+\sqrt2}-6\sqrt{4+2\sqrt2}}}{2} ≈ 3.69918 i$
Related polytopes
Army	Grotoct
Regiment	Grotoct
Dual	3-8 kisrhombille tiling
Abstract & topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[8,3]
Convex	Yes

The great rhombitrioctagonal tiling or grotoct, also called the truncated trioctagonal tiling, is a uniform tiling of the hyperbolic plane. 1 square, 1 hexagon and 1 hexadecagon join at each vertex. It can be formed by cantitruncation of either the octagonal tiling or its dual order-8 triangular tiling, or equivalently by truncation 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. "grotoct".

• Wikipedia Contributors. "Truncated trioctagonal tiling".