# Small dodecicosahedral prism

Small dodecicosahedral prism
Rank4
TypeUniform
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${\displaystyle {\sqrt {\frac {19+3{\sqrt {5}}}{8}}}\approx 1.79263}$
Dichoral anglesSiddy–6–hip: 90°
Siddy–10–dip: 90°
Hip–4–dip #1: ${\displaystyle \arccos \left({\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 79.18768^{\circ }}$
Hip–4–dip #2: ${\displaystyle \arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 37.37737^{\circ }}$
Height1
Number of external pieces504
Related polytopes
ArmySemi-uniform Sriddip
RegimentSiidip
DualSmall dodecicosacronic tegum
ConjugateGreat dodecicosahedral prism
Abstract & topological properties
Euler characteristic–30
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.