# Great dodecahedral prism

Great dodecahedral prism
Rank4
TypeUniform
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${\displaystyle {\sqrt {\frac {7+{\sqrt {5}}}{8}}}\approx 1.07448}$
Hypervolume${\displaystyle {\frac {5+3{\sqrt {5}}}{4}}\approx 2.92705}$
Pip–4–pip: ${\displaystyle \arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }}$
Height1
Central density3
Number of external pieces62
Related polytopes
ArmyIpe
RegimentIpe
DualSmall stellated dodecahedral tegum
ConjugateSmall stellated dodecahedral prism
Abstract & topological properties
Euler characteristic–8
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.