Order-6 dodecahedral honeycomb

Order-6 dodecahedral honeycomb
Rank	4
Type	Regular, paracompact
Space	Hyperbolic
Notation
Bowers style acronym	Hedhon
Coxeter diagram	x5o3o6o ()
Schläfli symbol	{5,3,6}
Elements
Cells	NM dodecahedra
Faces	6NM pentagons
Edges	5NM
Vertices	10N
Vertex figure	Triangular tiling, edge length (1+√5)/2
Measures (edge length 1)
Circumradius	0
Related polytopes
Army	Hedhon
Regiment	Hedhon
Dual	Order-5 hexagonal tiling honeycomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	[6,3,5]
Convex	Yes

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

Representations[edit | edit source]

An order-6 dodecahedral honeycomb has the followig Coxeter diagrams:

x5o3o6o () (full symmetry)
x5o3o3o3*b () (dodecahedra of two different types)

Related polytopes[edit | edit source]

o6o3o5o truncations
Name	OBSA	Schläfli symbol
Order-5 hexagonal tiling honeycomb	phexah	{6,3,5}
Truncated order-5 hexagonal tiling honeycomb	tiphexah	t{6,3,5}
Rectified order-5 hexagonal tiling honeycomb	riphexah	r{6,3,5}
Dodecahedral-hexagonal tiling honeycomb	dohexah	2t{6,3,5}
Rectified order-6 dodecahedral honeycomb	rihed	r{5,3,6}
Truncated order-6 dodecahedral honeycomb	thed	t{5,3,6}
Order-6 dodecahedral honeycomb	hedhon	{5,3,6}
Small rhombated order-5 hexagonal tiling honeycomb	sriphexah	rr{6,3,5}
Great rhombated order-5 hexagonal tiling honeycomb	griphexah	tr{6,3,5}
Small rhombated order-6 dodecahedral honeycomb	srihed	rr{5,3,6}
Great rhombated order-6 dodecahedral honeycomb	grihed	tr{5,3,6}
Small prismated order-5 hexagonal tiling honeycomb	sidpidohexah	t_0,3{6,3,5}
Prismatorhombated order-6 dodecahedral honeycomb	prihed	t_0,1,3{6,3,5}
Prismatorhombated order-5 hexagonal tiling honeycomb	priphaxh	t_0,1,3{5,3,6}
Great prismated order-5 hexagonal tiling honeycomb	gidpidohaxh	t_0,1,2,3{6,3,5}