Order-4 hexagonal tiling

Order-4 hexagonal tiling
Rank	3
Type	Regular
Space	Hyperbolic
Notation
Bowers style acronym	Shexat
Coxeter diagram	x6o4o ()
Schläfli symbol	{6,4}
Elements
Faces	2N hexagons
Edges	6N
Vertices	3N
Vertex figure	Square, edge length √3
Measures (edge length 1)
Circumradius	$\frac{i\sqrt{2}}{2} ≈ 0.70711 i$
Related polytopes
Army	Shexat
Regiment	Shexat
Dual	Order-6 square tiling
Topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[6,4]
Convex	Yes

The order-4 hexagonal tiling is a regular tiling of the hyperbolic plane. 4 hexagons join at each vertex.

It can be formed by rectifying the order-6 hexagonal tiling.

Representations

The order-4 hexagonal tiling has the following Coxeter diagrams:

• x6o4o (full symmetry)
• o6x6o () (as rectified order-6 hexagonal tiling)
• x3x6o6*a (hexagons of 3 types, trapezivert)

Related polytopes

o6o4o truncations

Name	OBSA	Schläfli symbol	CD diagram	Picture
Order-4 hexagonal tiling	shexat	{6,4}	x6o4o
Truncated order-4 hexagonal tiling	toshexat	t{6,4}	x6x4o
Tetrahexagonal tiling	tehat	r{6,4}	o6x4o
Truncated order-6 square tiling	thisquat	t{4,6}	o6x4x
Order-6 square tiling	hisquat	{4,6}	o6o4x
Small rhombitetrahexagonal tiling	srotehat	rr{6,4}	x6o4x
Great rhombitetrahexagonal tiling	grotehat	tr{6,4}	x6x4x
Snub tetrahexagonal tiling	snatehat	sr{6,4}	s6s4s

External links

• Klitzing, Richard. "Shexat".

• Wikipedia Contributors. "Order-4 hexagonal tiling".