Order-6 hexagonal tiling

Order-6 hexagonal tiling
Rank	3
Type	Regular
Space	Hyperbolic
Notation
Bowers style acronym	Hihexat
Coxeter diagram	x6o6o ()
Schläfli symbol	{6,6}
Elements
Faces	N hexagons
Edges	3N
Vertices	N
Vertex figure	Hexagon, edge length √3
Measures (edge length 1)
Circumradius	$\frac{i\sqrt2}{4} ≈ 0.35355 i$
Related polytopes
Army	Hihexat
Regiment	Hihexat
Dual	Order-6 hexagonal tiling
Topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	[6,6]
Convex	Yes

The order-6 hexagonal tiling is a regular tiling of the hyperbolic plane. 6 hexagons join at each vertex. It is self-dual.

It can be formed by alternating the order-6 square tiling.

Representations

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

• x6o6o (main symmetry)
• s4o6o () (as alternated order-6 square tiling)
• o3o4s4*a ( ) (alternating order-6 square tiling with half symmetry)
• o3o6x6*a ( ) (hexagons of two types)

Related polytopes

o6o6o truncations

Name	OBSA	Schläfli symbol	CD diagram	Picture
Order-6 hexagonal tiling	hihat	{6,6}	x6o6o
Truncated order-6 hexagonal tiling	thihat	t{6,6}	x6x6o
Hexahexagonal tiling = Order-4 hexagonal tiling	shexat	r{6,6}	o6x6o
Truncated order-6 hexagonal tiling	thihat	t{6,6}	o6x6x
Order-6 hexagonal tiling	hihat	{6,6}	o6o6x
Small rhombihexahexagonal tiling = Tetrahexagonal tiling	tehat	rr{6,6}	x6o6x
Great rhombitetrahexagonal tiling = Truncated order-4 hexagonal tiling	toshexat	tr{6,6}	x6x6x
Snub hexahexagonal tiling	shihat	sr{6,6}	s6s6s

External links

• Klitzing, Richard. "Hihexat".

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