# Great quasitruncated icosidodecahedral prism

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Great quasitruncated icosidodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymGaquatiddip
Coxeter diagramx x5/3x3x ()
Elements
Cells30 cubes, 20 hexagonal prisms, 12 decagrammic prisms, 2 great quasitruncated icosidodecahedra
Faces60+60+60+60 squares, 40 hexagons, 24 decagrams
Edges120+120+120+120
Vertices240
Vertex figureIrregular tetrahedron, edge lengths 2, 3, (5–5)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {8-3{\sqrt {5}}}}\approx 1.13657}$
Hypervolume${\displaystyle 5(10{\sqrt {5}}-19)\approx 16.80340}$
Dichoral anglesCube–4–stiddip: ${\displaystyle \arccos \left(-{\sqrt {\frac {5-{\sqrt {5}}}{10}}}\right)\approx 121.71747^{\circ }}$
Gaquatid–10/3–stiddip: 90°
Gaquatid–6–hip: 90°
Gaquatid–4–cube: 90°
Hip–4–stiddip: ${\displaystyle \arccos \left({\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 79.18768^{\circ }}$
Cube–4–hip: ${\displaystyle \arccos \left({\frac {{\sqrt {15}}-{\sqrt {3}}}{6}}\right)\approx 69.09484^{\circ }}$
Height1
Central density13
Number of external pieces1142
Related polytopes
ArmySemi-uniform Griddip
RegimentGaquatiddip
DualGreat disdyakis triacontahedral tegum
ConjugateGreat rhombicosidodecahedral prism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The great quasitruncated icosidodecahedral prism or gaquatiddip, is a prismatic uniform polychoron that consists of 2 great quasitruncated icosidodecahedra, 12 decagrammic prisms, 20 hexagonal prisms, and 30 cubes. Each vertex joins one of each type of cell. as the name suggests, it is a prism based on the great quasitruncated icosidodecahedron.

The great rhombicosidodecahedral pirsm can be vertex-inscribed into the great tritrigonary hexacositrishecatonicosachoron.

## Vertex coordinates

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

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

along with all even permutations of the first three coordinates of:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {4-{\sqrt {5}}}{2}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm 1,\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {7-3{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm 3{\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {3-{\sqrt {5}}}{2}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}}\right).}$