Rank4
TypeUniform
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${\displaystyle {\frac {\sqrt {5}}{2}}\approx 1.11803}$
Hypervolume5
Dichoral anglesPip–4–stip: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }}$
Did–5–pip: 90°
Did–5/2–stip: 90°
Height1
Central density3
Number of external pieces74
Related polytopes
ArmySemi-uniform Iddip
RegimentDiddip
DualMedial rhombic triacontahedral tegum
Abstract & topological properties
Euler characteristic–8
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:

• ${\displaystyle \left(\pm 1,\,0,\,0,\,\pm {\frac {1}{2}}\right),}$

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

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