Order-5 hexagonal tiling honeycomb

Order-5 hexagonal tiling honeycomb
Rank	4
Type	Regular, paracompact
Space	Hyperbolic
Notation
Bowers style acronym	Phexah
Coxeter diagram	x6o3o5o ()
Schläfli symbol	{6,3,5}
Elements
Cells	10N hexagonal tilings
Faces	5NM hexagons
Edges	6NM
Vertices	NM
Vertex figure	Icosahedron, edge length √3
Measures (edge length 1)
Circumradius
Related polytopes
Army	Phexah
Regiment	Phexah
Dual	Order-6 dodecahedral honeycomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	[6,3,5]
Convex	Yes

The order-5 hexagonal tiling honeycomb is a paracompact regular tiling of 3D hyperbolic space. Each cell is a hexagonal tiling whose vertices lie on a horosphere, a surface in hyperbolic space that approaches a single ideal point at infinity. 5 hexagonal tilings meet at each edge, and 20 meet at each vertex.

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}