# Great icosihemidodecahedral prism

The great icosihemidodecahedral prism or geihiddip, is a prismatic uniform polychoron that consists of 2 great icosihemidodecahedra, 20 triangular prisms, and 6 decagrammic prisms. Each vertex joins 1 great icosihemidodecahedron, 2 triangular prisms, and 2 decagrammic prisms. As the name suggests, it is a prism based on the great icosihemidodecahedron.

Great icosihemidodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymGeihiddip
Coxeter diagram/2 ((x x5/3x3/2o3*b)/2)
Elements
Cells20 triangular prisms, 6 decagrammic prisms, 2 great icosihemidodecahedra
Faces40 triangles, 60 squares, 12 decagrams
Edges30+120
Vertices60
Vertex figureBowtie pyramid, edge lengths 1, (5–5)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {7-2{\sqrt {5}}}}{2}}\approx 0.79496}$
Dichoral anglesGeihid–3–trip: 90°
Geihid–10/3–stiddip: 90°
Trip–4–stiddip: ${\displaystyle \arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 37.37737^{\circ }}$
Height1
Number of external pieces182
Related polytopes
ArmySemi-uniform Iddip
RegimentGiddip
DualGreat icosihemidodecacronic tegum
ConjugateSmall icosihemidodecahedral prism
Abstract & topological properties
Euler characteristic–2
OrientableNo
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

## Vertex coordinates

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