Great rhombihexahedral prism

Great rhombihexahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Grohp
Elements
Cells	12 cubes, 6 octagrammic prisms, 2 great rhombihexahedra
Faces	24+24+24 squares, 12 octagrams
Edges	24+48+48
Vertices	48
Vertex figure	Butterfly pyramid, edge lengths √2, √2–√2, √2, √2–√2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{3-\sqrt2}{2}} ≈ 0.89045$
Dichoral angles	Groh–4–cube: 90°
	Groh–8/3–stop: 90°
	Cube–4–stop #1: 90°
	Cube–4–stop #2: 45°
Height	1
Number of pieces	200
Related polytopes
Army	Semi-uniform Ticcup
Regiment	Goccope
Dual	Great rhombihexacronic tegum
Conjugate	Small rhombihexahedral prism
Abstract properties
Euler characteristic	–8
Topological properties
Orientable	No
Properties
Symmetry	B3×A1, order 96
Convex	No
Nature	Tame

The great rhombihexahedral prism or grohp is a prismatic uniform polychoron that consists of 2 great rhombihexahedra, 12 cubes, and 6 octagrammic prisms. Each vertex joins 1 great rhombihexahedron, 2 cubes, and 2 octagrammic prisms. As the name suggests, it is a prism based on the great rhombihexahedron.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 19: Prisms" (#934).

• Klitzing, Richard. "grohp".