# Great dodecahemicosahedral prism

Great dodecahemicosahedral prism
Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGidhipe
Coxeter diagram(x o5/4x3x5*b)/2 (/2)
Elements
Cells12 pentagonal prisms, 10 hexagonal prisms, 2 great dodecahemicosahedra
Faces60 squares, 24 pentagons, 20 hexagons
Edges30+120
Vertices60
Vertex figureBowtie pyramid, edge lengths (1+5)/2, 3 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt5}{2} ≈ 1.11803}$
Dichoral anglesGidhei–5–pip: 90°
Gidhei–6–hip: 90°
Pip–4–hip: ${\displaystyle \arccos\left(\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 37.37737°}$
Height1
Number of pieces314
Related polytopes
ArmySemi-uniform Iddip
RegimentDiddip
DualGreat dodecahemicosacronic tegum
ConjugateSmall dodecahemicosahedral prism
Abstract properties
Euler characteristic–10
Topological properties
OrientableNo
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

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.