# Great icosidodecahedral prism

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Great icosidodecahedral prism
Rank4
TypeUniform
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${\displaystyle {\frac {\sqrt {7-2{\sqrt {5}}}}{2}}\approx 0.79496}$
Hypervolume${\displaystyle {\frac {45-17{\sqrt {5}}}{6}}\approx 1.16447}$
Dichoral anglesTrip–4–stip: ${\displaystyle \arccos \left(-{\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 100.81232^{\circ }}$
Gid–3–trip: 90°
Gid–5/2–stip: 90°
Height1
Central density7
Number of external pieces134
Related polytopes
ArmySemi-uniform Iddip
RegimentGiddip
DualGreat rhombic triacontahedral tegum
ConjugateIcosidodecahedral prism
Abstract & topological properties
Euler characteristic0
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:

• ${\displaystyle \left(0,\,0,\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {1}{2}}\right),}$

along with all even permutations and all sign changes of the first three coordinates of:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}}\right).}$