Great rhombicosidodecahedral prism

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Great rhombicosidodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymGriddip
Coxeter diagramx x5x3x ()
Elements
Cells30 cubes, 20 hexagonal prisms, 12 decagonal prisms, 2 great rhombicosidodecahedra
Faces60+60+60+60 squares, 40 hexagons, 24 decagons
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–hip:
 Cube–4–dip:
 Hip–4–dip:
 Grid–10–dip: 90°
 Grid–6–hip: 90°
 Grid–4–cube: 90°
Height1
Central density1
Number of external pieces64
Level of complexity24
Related polytopes
ArmyGriddip
RegimentGriddip
DualDisdyakis triacontahedral tegum
ConjugateGreat quasitruncated icosidodecahedral prism
Abstract & topological properties
Flag count5760
Euler characteristic0
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexYes
NatureTame

The great rhombicosidodecahedral prism or griddip is a prismatic uniform polychoron that consists of 2 great rhombicosidodecahedra, 12 decagonal prisms, 20 hexagonal prisms, and 30 cubes. Each vertex joins one of each type of cell. It is a prism based on the great rhombicosidodecahedron. As such it is also a convex segmentochoron (designated K-4.150 on Richard Klitzing's list).

This polychoron can be alternated into a snub dodecahedral antiprism, which cannot be made uniform.

The great rhombicosidodecahedral prism can be vertex-inscribed into the small tritrigonary prismatohecatonicosidishexacosichoron.

Gallery[edit | edit source]

Vertex coordinates[edit | edit source]

The vertices of a great rhombicosidodecahedral 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:

Representations[edit | edit source]

A great rhombicosidodecahedral prism has the following Coxeter diagrams:

  • x x5x3x (full symmetry)
  • xx5xx3xx&#x (bases considered separately)

External links[edit | edit source]