Great dodecahemicosahedral prism

Great dodecahemicosahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gidhipe
Coxeter diagram	(x o5/4x3x5*b)/2 (/2)
Elements
Cells	12 pentagonal prisms, 10 hexagonal prisms, 2 great dodecahemicosahedra
Faces	60 squares, 24 pentagons, 20 hexagons
Edges	30+120
Vertices	60
Vertex figure	Bowtie pyramid, edge lengths (1+√5)/2, √3 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\frac{\sqrt5}{2} ≈ 1.11803$
Dichoral angles	Gidhei–5–pip: 90°
	Gidhei–6–hip: 90°
	Pip–4–hip: $\arccos\left(\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 37.37737°$
Height	1
Number of pieces	314
Related polytopes
Army	Semi-uniform Iddip
Regiment	Diddip
Dual	Great dodecahemicosacronic tegum
Conjugate	Small dodecahemicosahedral prism
Abstract properties
Euler characteristic	–10
Topological properties
Orientable	No
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The great dodecahemicosahedral prism or gidhipe, is a prismatic uniform polychoron that consists of 2 great dodecahemicosahedra, 12 pentagonal prisms, and 10 hexagonal prisms. Each vertex joins 1 great dodecahemicosahedron, 2 pentagonal prisms, and 2 hexagonal prisms. As the name suggests, it is a prism based on the great dodecahemicosahedron.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 19: Prisms" (#916).