# Great icosidodecahedral prism

Great icosidodecahedral prism Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGiddip
Coxeter diagramx o5/2x3o (         )
Elements
Cells20 triangular prisms, 12 pentagrammic prisms, 2 great icosidodecahedra
Faces40 triangles, 60 squares, 24 pentagrams
Edges30+120
Vertices60
Vertex figureRectangular pyramid, edge lengths 1, (5–1)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius$\frac{\sqrt{7-2\sqrt5}}{2} ≈ 0.79496$ Hypervolume$\frac{45-17\sqrt5}{6} ≈ 1.16447$ Dichoral anglesTrip–4–stip: $\arccos\left(-\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 100.81232°$ Gid–3–trip: 90°
Gid–5/2–stip: 90°
Height1
Central density7
Number of pieces134
Related polytopes
ArmySemi-uniform Iddip
RegimentGiddip
DualGreat rhombic triacontahedral tegum
ConjugateIcosidodecahedral prism
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The great icosidodecahedral prism or giddip, is a prismatic uniform polychoron that consists of 2 great icosidodecahedra, 12 pentagrammic prisms, and 20 triangular prisms. Each vertex joins 1 great icosidodecahedron, 2 pentagrammic prisms, and 2 triangular prisms. As the name suggests, it is a prism based on the great icosidodecahedron.

## Vertex coordinates

The vertices of a great icosidodecahedral prism of edge length 1 are given by all permutations and sign changes of the first three coordinates of:

• $\left(0,\,0,\,±\frac{\sqrt5-1}{2},\,±\frac12\right),$ along with all even permutations and all sign changes of the first three coordinates of:

• $\left(±\frac12,\,±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{4},\,±\frac12\right).$ 