Great icosahedral prism

Great icosahedral prism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gipe
Coxeter diagram	x o5/2o3x ()
Elements
Cells	20 triangular prisms, 2 great icosahedra
Faces	40 triangles, 30 squares
Edges	12+60
Vertices	24
Vertex figure	Pentagrammic pyramid, edge lengths 1 (base), √2 (legs)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {7-{\sqrt {5}}}{8}}}\approx 0.77168$
Hypervolume	$5{\frac {3-{\sqrt {5}}}{12}}\approx 0.31831$
Dichoral angles	Gike–3–trip: 90°
	Trip–4–trip: $\arccos \left({\frac {\sqrt {5}}{3}}\right)\approx 41.81031^{\circ }$
Height	1
Central density	7
Number of external pieces	182
Related polytopes
Army	Semi-uniform Ipe
Regiment	Sissiddip
Dual	Great stellated dodecahedral tegum
Conjugate	Icosahedral prism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The great icosahedral prism or gipe is a prismatic uniform polychoron that consists of 2 great icosahedra and 20 triangular prisms. Each vertex joins 1 great icosahedron and 5 triangular prisms. As the name suggests, it is a prism based on the great icosahedron.

Cross-sections

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small stellated dodecahedral prism.

External links

• Bowers, Jonathan. "Category 19: Prisms" (#895).

• Klitzing, Richard. "gipe".