# Great icosicosidodecahedral prism

Great icosicosidodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymGiidip
Coxeter diagramx o3/2x3x5*b ()
Elements
Cells20 triangular prisms, 12 pentagonal prisms, 20 hexagonal prisms, 2 great icosicosidodecahedra
Faces40 triangles, 60+60 squares, 24 pentagons, 40 hexagons
Edges60+120+120
Vertices120
Vertex figureCrossed isosceles trapezoidal pyramid, edge lengths 1, 3, (1+5)/2, 3 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {19-3{\sqrt {5}}}{8}}}\approx 1.23955}$
Hypervolume${\displaystyle {\frac {29{\sqrt {5}}-30}{3}}\approx 11.61533}$
Dichoral anglesPip–4–hip: ${\displaystyle \arccos \left(-{\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 100.81232^{\circ }}$
Giid–5–pip: 90°
Giid–3–trip: 90°
Giid–6–hip: 90°
Trip–4–hip: ${\displaystyle \arccos \left({\frac {\sqrt {5}}{3}}\right)\approx 41.81031^{\circ }}$
Height1
Central density6
Number of external pieces1234
Related polytopes
ArmySemi-uniform Tiddip
RegimentGidditdiddip
DualGreat icosacronic hexecontahedral bipyramid
ConjugateSmall icosicosidodecahedral prism
Abstract & topological properties
Euler characteristic–10
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The great icosicosidodecahedral prism or giidip is a prismatic uniform polychoron that consists of 2 great icosicosidodecahedra, 12 pentagonal prisms, 20 triangular prisms, and 20 hexagonal prisms. Each vertex joins 1 great icosicosidodecahedron, 1 pentagonal prism, 1 triangular prism, and 2 hexagonal prisms. As the name suggests, it is a prism based on the great icosicosidodecahedron.

## Vertex coordinates

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