Order-6 square tiling

Order-6 square tiling
Rank	3
Type	Regular
Space	Hyperbolic
Notation
Bowers style acronym	Hisquat
Coxeter diagram	o6o4x ()
Schläfli symbol	{4,6}
Elements
Faces	3N squares
Edges	6N
Vertices	2N
Vertex figure	Hexagon, edge length √2
Measures (edge length 1)
Circumradius	$\frac{i}{2} = 0.5 i$
Related polytopes
Army	Hisquat
Regiment	Hisquat
Dual	Order-4 hexagonal tiling
Topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[6,4]
Convex	Yes

The order-6 square tiling is a regular tiling of the hyperbolic plane. 6 squares join at each vertex.

This tiling can be alternated to produce the regular order-6 hexagonal tiling.

Representations

The order-6 square tiling has the following Coxeter diagrams:

• o6o4x (full symmetry)
• o3o4x4*a (squares of two types)

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. "Hisquat".

• Wikipedia Contributors. "Order-6 square tiling".