Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymDiddip
Coxeter diagramx o5/2x5o ()
Elements
Cells12 pentagonal prisms, 12 pentagrammic prisms, 2 dodecadodecahedra
Faces60 squares, 24 pentagons, 24 pentagrams
Edges30+120
Vertices60
Vertex figureRectangular pyramid, edge lengths (1+5)/2, (5–1)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt5}{2} ≈ 1.11803}$
Hypervolume5
Dichoral anglesPip–4–stip: ${\displaystyle \arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505^\circ}$
Did–5–pip: 90°
Did–5/2–stip: 90°
Height1
Central density3
Number of pieces74
Related polytopes
ArmySemi-uniform Iddip
RegimentDiddip
DualMedial rhombic triacontahedral tegum
Abstract properties
Euler characteristic–8
Topological properties
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The dodecadodecahedral prism or diddip, is a prismatic uniform polychoron that consists of 2 dodecadodecahedra, 12 pentagrammic prisms, and 12 pentagonal prisms. Each vertex joins 1 dodecadodecahedron, 2 pentagrammic prisms, and 2 pentagonal prisms. As the name suggests, it is a prism based on the dodecadodecahedron.

## Vertex coordinates

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

• ${\displaystyle \left(±1,\,0,\,0,\,±\frac12\right),}$

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

• ${\displaystyle \left(±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac12,\,±\frac12\right).}$