# Great dodecahedral prism

Great dodecahedral prism
Rank4
TypeUniform
SpaceSpherical
Notation
Coxeter diagramx o5/2o5x ()
Elements
Cells12 pentagonal prisms, 2 great dodecahedra
Faces30 squares, 24 pentagons
Edges12+60
Vertices24
Vertex figurePentagrammic pyramid, edge lengths (1+5)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{7+\sqrt5}{8}} ≈ 1.07448}$
Hypervolume${\displaystyle \frac{5+3\sqrt5}{4} ≈ 2.92705}$
Pip–4–pip: ${\displaystyle \arccos\left(\frac{\sqrt5}{5}\right) ≈ 63.43495^\circ}$
Height1
Central density3
Number of pieces62
Related polytopes
ArmyIpe
RegimentIpe
DualSmall stellated dodecahedral tegum
ConjugateSmall stellated dodecahedral prism
Abstract properties
Euler characteristic–8
Topological properties
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The great dodecahedral prism or gaddip is a prismatic uniform polychoron that consists of 2 great dodecahedra and 12 pentagonal prisms. Each vertex joins 1 great dodecahedron and 5 pentagonal prisms. As the name suggests, it is a prism based on the great dodecahedron.

## Vertex coordinates

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