# Small dodecahemicosahedral prism

Small dodecahemicosahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymSidhipe
Coxeter diagram/2 ((x x5/3o5/2x3*b)/2)
Elements
Cells12 pentagrammic prisms, 10 hexagonal prisms, 2 small dodecahemicosahedra
Faces60 squares, 24 pentagrams, 20 hexagons
Edges30+120
Vertices60
Vertex figureBowtie pyramid, edge lengths (5–1)/2, 3 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {5}}{2}}\approx 1.11803}$
Dichoral anglesSidhei–5/2–stip: 90°
Sidhei–6–hip: 90°
Stip–4–hip: ${\displaystyle \arccos \left({\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 79.18768^{\circ }}$
Height1
Number of external pieces156
Related polytopes
ArmySemi-uniform Iddip
RegimentDiddip
DualSmall dodecahemicosacronic tegum
ConjugateGreat dodecahemicosahedral prism
Abstract & topological properties
Euler characteristic–10
OrientableNo
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The small dodecahemicosahedral prism or sidhipe, is a prismatic uniform polychoron that consists of 2 small dodecahemicosahedra, 12 pentagrammic prisms, and 10 hexagonal prisms. Each vertex joins 1 small dodecahemicosahedron, 2 pentagrammic prisms, and 2 hexagonal prisms. As the name suggests, it is a prism based on the small dodecahemicosahedron.

## Vertex coordinates

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