Quasitruncated dodecadodecahedral prism

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Quasitruncated dodecadodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymQuitdiddip
Coxeter diagramx x5/3x5x ()
Elements
Cells30 cubes, 12 decagonal prisms, 12 decagrammic prisms, 2 quasitruncated dodecadodecahedra
Faces60+60+60+60 squares, 24 decagons, 24 decagrams
Edges120+120+120+120
Vertices240
Vertex figureIrregular tetrahedron, edge lengths 2, (5+5)/2, (5–5)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume15
Dichoral anglesCube–4–stiddip:
 Quitdid–10/3–stiddip: 90°
 Quitdid–10–dip: 90°
 Quitdid–4–cube: 90°
 Dip–4–stiddip:
 Cube–4–dip:
Height1
Central density-3
Number of external pieces406
Related polytopes
ArmySemi-uniform Griddip
RegimentQuitdiddip
DualMedial disdyakis triacontahedral tegum
ConjugateQuasitruncated dodecadodecahedral prism
Abstract & topological properties
Euler characteristic–8
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The quasitruncated dodecadodecahedral prism or quitdiddip, is a prismatic uniform polychoron that consists of 2 quasitruncated dodecadodecahedra, 12 decagrammic prisms, 12 decagonal prisms, and 30 cubes. Each vertex joins one of each type of cell. as the name suggests, it is a prism based on the quasitruncated dodecadodecahedron.

The great rhombicosidodecahedral prism can be vertex-inscribed into the rectified small ditrigonary hexacosihecatonicosachoron.

Vertex coordinates[edit | edit source]

The vertices of a quasitruncated dodecadodecahedral 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]