# Small rhombidodecahedral prism

Small rhombidodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymSirdip
Elements
Cells30 cubes, 12 decagonal prisms, 2 small rhombidodecahedra
Faces60+60+60 squares, 24 decagons
Edges60+120+120
Vertices120
Vertex figureButterfly pyramid, edge lengths 2, (5+5)/2, 2, (5+5)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {{\sqrt {2}}+{\sqrt {10}}}{2}}\approx 2.28825}$
Dichoral anglesCube–4–dip #1: ${\displaystyle \arccos \left(-{\sqrt {\frac {5-{\sqrt {5}}}{10}}}\right)\approx 121.71747^{\circ }}$
Sird–4–cube: 90°
Sird–10–dip: 90°
Cube–4–dip #2: ${\displaystyle \arccos \left({\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)\approx 31.71747^{\circ }}$
Height1
Number of external pieces224
Related polytopes
ArmySriddip
RegimentSriddip
DualSmall rhombidodecacronic tegum
ConjugateGreat rhombidodecahedral prism
Abstract & topological properties
Euler characteristic–20
OrientableNo
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The small rhombidodecahedral prism or sirdip is a prismatic uniform polychoron that consists of 2 small rhombidodecahedra, 30 cubes, and 12 decagonal prisms. Each vertex joins 1 small rhombidodecahedron, 2 cubes, and 2 decagonal prisms. As the name suggests, it is a prism based on the small rhombidodecahedron.

## Vertex coordinates

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