Great rhombitetrahexagonal tiling

Great rhombitetrahexagonal tiling
Rank	3
Type	Uniform
Space	Hyperbolic
Notation
Bowers style acronym	Grotehat
Coxeter diagram	x6x4x ()
Elements
Faces	6N squares, 3N octagons, 2N dodecagons
Edges	12N+12N+12N
Vertices	24N
Vertex figure	Scalene triangle, edge lengths √2, √2+√2, (√2+√6)/2
Measures (edge length 1)
Circumradius
Related polytopes
Army	Grotehat
Regiment	Grotehat
Dual	4-6 kisrhombille tiling
Abstract & topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[6,4]
Convex	Yes

The great rhombitetrahexagonal tiling or grotehat, also called the truncated tetrahexagonal tiling or omnitruncated tetrahexagonal tiling, is a uniform tiling of the hyperbolic plane. 1 square, 1 octagon and 1 dodecagon join at each vertex. It can be formed by cantitruncation of either the order-4 hexagonal tiling or its dual order-6 square tiling, or equivalently by truncation of the tetrahexagonal tiling.

External links[edit | edit source]

v t e truncations
Name	OBSA	Schläfli symbol	CD diagram	Image
Order-4 hexagonal tiling	shexat	${6,4}$
Tetrahexagonal tiling	tehat	r ${6,4}$
Order-6 square tiling	hisquat	${4,6}$
Truncated order-4 hexagonal tiling	toshexat	t ${6,4}$
Small rhombitetrahexagonal tiling	srotehat	rr ${6,4}$
Truncated order-6 square tiling	thisquat	t ${4,6}$
Great rhombitetrahexagonal tiling	grotehat	tr ${6,4}$
Snub tetrahexagonal tiling	snatehat	sr ${6,4}$