Small rhombated icosahedral honeycomb

Small rhombated icosahedral honeycomb
Rank	4
Type	Uniform, compact
Space	Hyperbolic
Notation
Bowers style acronym	Srih
Coxeter diagram	x3o5x3o ()
Elements
Cells	10N triangular prisms, N icosidodecahedra, N small rhombicosidodecahedra
Faces	10N+20N triangles, 30N squares, 12N pentagons
Edges	30N+60N
Vertices	30N
Vertex figure	Rectangular wedge, edge lengths 1 (two edges of base rectangle and top edge), (1+√5)/2 (remaining base edges), and √2 (side edges)
Measures (edge length 1)
Circumradius
Related polytopes
Army	Srih
Regiment	Srih
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	[3,5,3]
Convex	Yes

The small rhombated icosahedral honeycomb or srih, also called the cantellated icosahedral honeycomb, is a compact uniform tiling of 3D hyperbolic space. 1 icosidodecahedron, 2 small rhombicosidodecahedra, and 2 triangular prisms meet at each vertex. As the name suggests, it can be derived by cantellation of the icosahedral honeycomb.

External links[edit | edit source]

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