# Truncated great icosahedral prism

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Truncated great icosahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymTiggipe
Coxeter diagramx o5/2x3x ()
Elements
Cells12 pentagrammic prisms, 20 hexagonal prisms, 2 truncated great icosahedra
Faces30+60 squares, 24 pentagrams, 40 hexagons
Edges60+60+120
Vertices120
Vertex figureSphenoid, edge lengths (5–1)/2, 3, 3 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {31-9{\sqrt {5}}}{8}}}\approx 1.16594}$
Hypervolume${\displaystyle {\frac {125-43{\sqrt {5}}}{4}}\approx 7.21227}$
Dichoral anglesStip–4–hip: ${\displaystyle \arccos \left(-{\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 100.81232^{\circ }}$
Tiggy–5/2–stip: 90°
Tiggy–6–hip: 90°
Hip–4–hip: ${\displaystyle \arccos \left({\frac {\sqrt {5}}{3}}\right)\approx 41.81031^{\circ }}$
Height1
Central density7
Number of external pieces1194
Related polytopes
ArmySemi-uniform Sriddip
RegimentTiggipe
DualGreat stellapentakis dodecahedral tegum
ConjugateTruncated icosahedral prism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The truncated great icosahedral prism or tiggipe is a prismatic uniform polychoron that consists of 2 truncated great icosahedra, 12 pentagrammic prisms, and 20 hexagonal prisms. Each vertex joins 1 truncated great icosahedron, 1 pentagrammic prism, and 2 hexagonal prisms. As the name suggests, it is a prism based on the truncated great icosahedron.

## Vertex coordinates

Coordinates for the vertices of a truncated great icosahedral prism of edge length 1 are given by all even permutations of the first three coordinates of:

• ${\displaystyle \left(0,\,\pm {\frac {1}{2}},\,\pm 3{\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm 1,\,\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {1}{2}}\right).}$