# Small dodecicosidodecahedral prism

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Small dodecicosidodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymSaddiddip
Coxeter diagramx x3/2o5x5*b ()
Elements
Cells20 triangular prisms, 12 pentagonal prisms, 12 decagonal prisms, 2 small dodecicosidodecahedra
Faces40 triangles, 60+60 squares, 24 pentagons, 24 decagons
Edges60+120+120
Vertices120
Vertex figureCrossed isosceles trapezoidal pyramid, edge lengths 1, (5+5)/2, (1+5)/2, (5+5)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {{\sqrt {2}}+{\sqrt {10}}}{2}}\approx 2.28825}$
Hypervolume${\displaystyle 2{\frac {45+17{\sqrt {5}}}{3}}\approx 55.34210}$
Dichoral anglesPip–4–dip: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }}$
Saddid–5–pip: 90°
Saddid–3–trip: 90°
Saddid–10–dip: 90°
Trip–4–dip: ${\displaystyle \arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 37.37737^{\circ }}$
Height1
Central density2
Number of external pieces194
Related polytopes
ArmySriddip
RegimentSriddip
DualSmall dodecacronic hexecontahedral tegum
ConjugateGreat dodecicosidodecahedral prism
Abstract & topological properties
Euler characteristic–18
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The small dodecicosidodecahedral prism or saddiddip is a prismatic uniform polychoron that consists of 2 small dodecicosidodecahedra, 12 pentagonal prisms, 20 triangular prisms, and 12 decagonal prisms. Each vertex joins 1 small dodecicosidodecahedron, 1 pentagonal prism, 1 triangular prism, and 2 decagonal prisms. As the name suggests, it is a prism based on the small dodecicosidodecahedron.

## Vertex coordinates

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