# Great rhombidodecahedral prism

Great rhombidodecahedral prism
Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGirdip
Elements
Cells30 cubes, 12 decagrammic prisms, 2 great rhombidodecahedra
Faces60+60+60 squares, 24 decagrams
Edges60+120+120
Vertices120
Vertex figureButterfly pyramid, edge lengths 2, (5–5)/2, 2, (5–5)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt{10}-\sqrt2}{2} \approx 0.87403}$
Dichoral anglesGird–4–cube: 90°
Gird–10/3–stiddip: 90°
Cube–4–stiddip #1: ${\displaystyle \arccos\left(\sqrt{\frac{5-\sqrt5}{10}}\right) \approx 58.28253°}$
Cube–4–stiddip #2: ${\displaystyle \arccos\left(\sqrt{\frac{5+\sqrt5}{10}}\right) \approx 31.71747°}$
Height1
Number of pieces1036
Related polytopes
ArmySemi-uniform Tipe
DualGreat rhombidodecacronic tegum
ConjugateSmall rhombidodecahedral prism
Abstract properties
Euler characteristic–20
Topological properties
OrientableNo
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The great rhombidodecahedral prism or girdip is a prismatic uniform polychoron that consists of 2 great rhombidodecahedra, 30 cubes, and 12 decagrammic prisms. Each vertex joins 1 great rhombidodecahedron, 2 cubes, and 2 decagrammic prisms. As the name suggests, it is a prism based on the great rhombidodecahedron.

## Vertex coordinates

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