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
Hypervolume
Dichoral anglesCube–4–stiddip:
 Gaquatid–10/3–stiddip: 90°
 Gaquatid–6–hip: 90°
 Gaquatid–4–cube: 90°
 Hip–4–stiddip:
 Cube–4–hip:
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[edit | edit source]

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

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

External links[edit | edit source]