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${\displaystyle {\sqrt {3}}\approx 1.73205}$
Hypervolume15
Dichoral anglesCube–4–stiddip: ${\displaystyle \arccos \left(-{\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)\approx 148.28253^{\circ }}$
Quitdid–10/3–stiddip: 90°
Quitdid–10–dip: 90°
Quitdid–4–cube: 90°
Dip–4–stiddip: ${\displaystyle \arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }}$
Cube–4–dip: ${\displaystyle \arccos \left({\sqrt {\frac {5-{\sqrt {5}}}{10}}}\right)\approx 58.28253^{\circ }}$
Height1
Central density-3
Number of external pieces406
Related polytopes
ArmySemi-uniform Griddip
RegimentQuitdiddip
DualMedial disdyakis triacontahedral tegum
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

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

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

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

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