# Small dodecicosahedral prism

Small dodecicosahedral prism
Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSiddipe
Elements
Cells20 hexagonal prisms, 12 decagonal prisms, 2 small dodecicosahedra
Faces60+60 squares, 40 hexagons, 24 decagons
Edges60+120+120
Vertices120
Vertex figureButterfly pyramid, edge lengths 3, (5+5)/2, 3, (5+5)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius$\sqrt{\frac{19+3\sqrt5}{8}} ≈ 1.79263$ Dichoral anglesSiddy–6–hip: 90°
Siddy–10–dip: 90°
Hip–4–dip #1: $\arccos\left(\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 79.18768°$ Hip–4–dip #2: $\arccos\left(\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 37.37737°$ Height1
Number of pieces504
Related polytopes
ArmySemi-uniform Sriddip
RegimentSiidip
DualSmall dodecicosacronic tegum
ConjugateGreat dodecicosahedral prism
Abstract properties
Euler characteristic–30
Topological properties
OrientableNo
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The small dodecicosahedral prism or siddipe is a prismatic uniform polychoron that consists of 2 small dodecicosahedra, 20 hexagonal prisms, and 12 decagonal prisms. Each vertex joins 1 small dodecicosahedron, 2 hexagonal prisms, and 2 decagonal prisms. As the name suggests, it is a prism based on the small dodecicosahedron.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small icosicosidodecahedral prism.