# Small icosicosidodecahedral prism

Small icosicosidodecahedral prism
Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSiidip
Coxeter diagramx x5/2o3x3*b ()
Elements
Cells20 triangular prisms, 12 pentagrammic prisms, 20 hexagonal prisms, 2 small icosicosidodecahedra
Faces40 triangles, 60+60 squares, 24 pentagrams, 40 hexagons
Edges60+120+120
Vertices120
Vertex figureIsosceles trapezoidal pyramid, edge lengths 1, 3, (5–1)/2, 3 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{19+3\sqrt5}{8}} ≈ 1.79263}$
Hypervolume${\displaystyle \frac{3)+29\sqrt5}{3} ≈ 31.61533}$
Dichoral anglesStip–4–hip: ${\displaystyle \arccos\left(-\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 142.62263°}$
Trip–4–hip: ${\displaystyle \arccos\left(-\frac{\sqrt5}{3}\right) ≈ 138.18969°}$
Siid–5/2–stip: 90°
Siid–3–trip: 90°
Siid–6–hip: 90°
Height1
Central density2
Number of pieces94
Related polytopes
ArmySemi-uniform Sriddip
RegimentSiidip
DualSmall icosacronic hexecontahedral tegum
ConjugateGreat icosicosidodecahedral prism
Abstract properties
Euler characteristic–10
Topological properties
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The small icosicosidodecahedral prism or siidip is a prismatic uniform polychoron that consists of 2 small icosicosidodecahedra, 12 pentagrammic prisms, 20 triangular prisms, and 20 hexagonal prisms. Each vertex joins 1 small icosicosidodecahedron, 1 pentagrammic prism, 1 triangular prism, and 2 hexagonal prisms. As the name suggests, it is a prism based on the small icosicosidodecahedron.

## Vertex coordinates

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

• ${\displaystyle \left(±\frac12,\,±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac12\right),}$
• ${\displaystyle \left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±\frac12\right),}$
• ${\displaystyle \left(±\frac12,\,±1,\,±\frac{3+\sqrt5}{4},\,±\frac12\right).}$