# Small dodecahemidodecahedral prism

Small dodecahemidodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymSidhiddip
Coxeter diagram/2 ((x x5/4o5x5*b)/2)
Elements
Cells12 pentagonal prisms, 6 decagonal prisms, 2 small dodecahemidodecahedra
Faces60 squares, 24 pentagons, 12 decagons
Edges30+120
Vertices60
Vertex figureBowtie pyramid, edge lengths (1+5)/2, (5+5)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {7+2{\sqrt {5}}}}{2}}\approx 1.69353}$
Dichoral anglesSidhid–5–pip: 90°
Sidhid–10–dip: 90°
Pip–4–dip: ${\displaystyle \arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }}$
Height1
Number of external pieces96
Related polytopes
ArmyIddip
RegimentIddip
DualSmall dodecahemidodecacronic tegum
ConjugateGreat dodecahemidodecahedral prism
Abstract & topological properties
Euler characteristic–14
OrientableNo
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The small dodecahemidodecahedral prism or sidhiddip, is a prismatic uniform polychoron that consists of 2 small dodecahemidodecahedra, 12 pentagonal prisms, and 6 decagonal prisms. Each vertex joins 1 small dodecahemidodecahedron, 2 pentagonal prisms, and 2 decagonal prisms. As the name suggests, it is a prism based on the small dodecahemidodecahedron.

## Vertex coordinates

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