Order-6 hexagonal tiling honeycomb

Order-6 hexagonal tiling honeycomb
Rank	4
Type	Regular, paracompact
Space	Hyperbolic
Notation
Bowers style acronym	Hihexah
Coxeter diagram	x6o3o6o ()
Schläfli symbol	{6,3,6}
Elements
Cells	2NK hexagonal tilings
Faces	NMK hexagons
Edges	2NMK
Vertices	2NK
Vertex figure	Triangular tiling, edge length √3
Measures (edge length 1)
Circumradius	0
Related polytopes
Army	Hihexah
Regiment	Hihexah
Dual	Order-6 hexagonal tiling honeycomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	[6,3,6]
Convex	Yes

The order-6 hexagonal tiling honeycomb is a paracompact regular tiling of 3D hyperbolic space. 6 ideal hexagonal tilings meet at each edge. All vertices are ideal points at infinity, with infinitely many hexagonal tilings meeting at each vertex in a triangular tiling arrangement.

Representations

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

• x6o3o6o () (full symmetry)
• x6o3o3o3*b () (hexagonal tilings of two types)

Related polytopes

o6o3o6o truncations

Name	OBSA	Schläfli symbol	CD diagram	Picture
Order-6 hexagonal tiling honeycomb	hihexah	{6,3,6}
Truncated order-6 hexagonal tiling honeycomb	thihexah	t{6,3,6}
Rectified order-6 hexagonal tiling honeycomb	rihihexah	r{6,3,6}
Dishexagonal tiling honeycomb = Hexagonal tiling honeycomb	hexah	2t{6,3,6}
Rectified order-6 hexagonal tiling honeycomb	rihihexah	r{6,3,6}
Truncated order-6 hexagonal tiling honeycomb	thihexah	t{6,3,6}
Order-6 hexagonal tiling honeycomb	hihexah	{6,3,6}
Small rhombated order-6 hexagonal tiling honeycomb	srihihexah	rr{6,3,6}
Great rhombated order-6 hexagonal tiling honeycomb	grihihexah	tr{6,3,6}
Small rhombated order-6 hexagonal tiling honeycomb	srihihexah	rr{6,3,6}
Great rhombated order-6 hexagonal tiling honeycomb	grihihexah	tr{6,3,6}
Small prismated order-6 hexagonal tiling honeycomb	spiddihexah	t0,3{6,3,6}
Prismatorhombated order-6 hexagonal tiling honeycomb	prihihexah	t0,1,3{6,3,6}
Prismatorhombated order-6 hexagonal tiling honeycomb	prihihexah	t0,1,3{6,3,6}
Great prismated order-6 hexagonal tiling honeycomb	gipiddihexah	t0,1,2,3{6,3,6}

External links

• Klitzing, Richard. "hihexah".

• Wikipedia Contributors. "Order-6 hexagonal tiling honeycomb".
• lllllllllwith10ls. "Category 1: Regulars" (#11).