The icosidodecadodecahedral prism or ididdip is a prismatic uniform polychoron that consists of 2 icosidodecadodecahedra, 12 pentagonal prisms, 12 pentagrammic prisms, and 20 hexagonal prisms. Each vertex joins 1 icosidodecadodecahedron, 1 pentagonal prism, 1 pentagrammic prism, and 2 hexagonal prisms. As the name suggests, it is a prism based on the icosidodecadodecahedron.

Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymIdiddip
Coxeter diagramx o5/3x3x5*b ()
Elements
Cells12 pentagonal prisms, 12 pentagrammic prisms, 20 hexagonal prisms, 2 icosidodecadodecahedra
Faces60+60 squares, 24 pentagons, 24 pentagrams, 40 hexagons
Edges60+120+120
Vertices120
Vertex figureCrossed isosceles trapezoidal pyramid, edge lengths (5–1)/2, 3, (1+5)/2, 3 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle \sqrt2 ≈ 1.41421}$
Hypervolume20
Dichoral anglesPip–4–hip: ${\displaystyle \arccos\left(-\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 100.81232^\circ}$
Ided–5/2–stip: 90°
Ided–5–pip: 90°
Ided–6–hip: 90°
Stip–4–hip: ${\displaystyle \arccos\left(\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 37.37737^\circ}$
Height1
Central density4
Number of external pieces434
Related polytopes
ArmySemi-uniform Tipe