Icosahedral honeycomb

Icosahedral honeycomb
Rank	4
Type	Regular, compact
Space	Hyperbolic
Notation
Bowers style acronym	Ikhon
Coxeter diagram	x3o5o3o ()
Schläfli symbol	{3,5,3}
Elements
Cells	N icosahedra
Faces	10N Triangles
Edges	10N
Vertices	N
Vertex figure	Dodecahedron, edge length 1
Measures (edge length 1)
Circumradius
Related polytopes
Army	Ikhon
Regiment	Ikhon
Dual	Order-3 icosahedral honeycomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	[3,5,3]
Convex	Yes

The order-3 icosahedral honeycomb, or just icosahedral honeycomb or ikhon, is a compact regular tiling of 3D hyperbolic space. 3 icosahedra meet at an edge, and 12 meet at a vertex. It is self-dual.

External links[edit | edit source]

Klitzing, Richard. "Ikhon".

Wikipedia Contributors. "Icosahedral honeycomb".
lllllllllwith10ls. "Category 1: Regulars" (#1).

v t e truncations
Name	OBSA	Schläfli symbol	CD diagram	Image
Icosahedral honeycomb	ikhon	${3,5,3}$
Rectified icosahedral honeycomb	rih	r ${3,5,3}$
Rectified icosahedral honeycomb	rih	r ${3,5,3}$
Icosahedral honeycomb	ikhon	${3,5,3}$
Truncated icosahedral honeycomb	tih	t ${3,5,3}$
Small rhombated icosahedral honeycomb	srih	rr ${3,5,3}$
Small prismated icosahedral honeycomb	spih	t_0,3 ${3,5,3}$
Disicosahedral honeycomb	dih	2t ${3,5,3}$
Small rhombated icosahedral honeycomb	srih	rr ${3,5,3}$
Truncated icosahedral honeycomb	tih	t ${3,5,3}$
Great rhombated icosahedral honeycomb	grih	tr ${3,5,3}$
Prismatorhombated icosahedral honeycomb	prih	t_0,1,3 ${3,5,3}$
Prismatorhombated icosahedral honeycomb	prih	t_0,2,3 ${3,5,3}$
Great rhombated icosahedral honeycomb	grih	tr ${3,5,3}$
Great prismated icosahedral honeycomb	gipiddih	t_0,1,2,3 ${3,5,3}$
Partially diminished icosahedral honeycomb	pidih

Icosahedral honeycomb

External links[edit | edit source]

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