Prismatorhombated icosahedral honeycomb

Prismatorhombated icosahedral honeycomb
Rank	4
Type	Uniform, compact
Space	Hyperbolic
Notation
Bowers style acronym	Prih
Coxeter diagram	x3x5o3x ()
Elements
Cells	10N triangular prisms, 10N hexagonal prisms, N truncated icosahedra, N small rhombicosidodecahedra
Faces	20N triangles, 30N+30N squares, 12N pentagons, 20N hexagons
Edges	30N+60N+60N
Vertices	60N
Vertex figure	Isosceles trapezoidal pyramid, base edge lengths 1, √2, (1+√5)/2, √2; lateral edge lengths √3, √3, √2, √2
Measures (edge length 1)
Circumradius
Related polytopes
Army	Prih
Regiment	Prih
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	[3,5,3]
Convex	Yes

The prismatorhombated icosahedral honeycomb or prih, also called the runcitruncated icosahedral honeycomb, is a compact uniform tiling of 3D hyperbolic space. 1 triangular prism, 2 hexagonal prisms, 1 truncated icosahedron, and 1 small rhombicosidodecahedron meet at each vertex. As the name suggests, it can be derived by runcitruncation or runcicantellation 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