Rhombicosahedral prism

Rhombicosahedral prism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Ripe
Elements
Cells	30 cubes, 20 hexagonal prisms, 2 rhombicosahedra
Faces	60+60+60 squares, 40 hexagons
Edges	60+120+120
Vertices	120
Vertex figure	Butterfly pyramid, edge lengths √2, √3, √2, √3 (base), √2 (legs)
Measures (edge length 1)
Circumradius	${\sqrt {2}}\approx 1.41421$
Dichoral angles	Cube–4–hip #1: $\arccos \left({\frac {{\sqrt {3}}-{\sqrt {15}}}{6}}\right)\approx 110.90516^{\circ }$
	Ri–4–cube: 90°
	Ri–6–hip: 90°
	Cube–4–hip #2: $\arccos \left({\frac {{\sqrt {3}}+{\sqrt {15}}}{6}}\right)\approx 20.90516^{\circ }$
Height	1
Related polytopes
Army	Semi-uniform Tipe
Regiment	Radiddip
Dual	Rhombicosacronic tegum
Conjugate	Rhombicosahedral pirsm
Abstract & topological properties
Euler characteristic	–12
Orientable	No
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The rhombicosahedral prism or ripe is a prismatic uniform polychoron that consists of 2 rhombicosahedra, 30 cubes, and 20 hexagonal prisms. Each vertex joins 1 rhombicosahedron, 2 cubes, and 2 hexagonal prisms. As the name suggests, it is a prism based on the rhombicosahedron.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the rhombidodecadodecahedral prism.

External links

• Bowers, Jonathan. "Category 19: Prisms" (#931).