# Small stellated dodecahedral prism

Small stellated dodecahedral prism Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSissiddip
Coxeter diagramx x5/2o5o (       )
Elements
Cells12 pentagrammic prisms, 2 small stellated dodecahedra
Faces30 squares, 24 pentagrams
Edges12+60
Vertices24
Vertex figurePentagonal pyramid, edge lengths (5–1)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius$\sqrt{\frac{7-\sqrt5}{8}} ≈ 0.77168$ Hypervolume$\frac{3\sqrt5-5}{4} ≈ 0.42705$ Dichoral anglesStip–4–stip: $\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505^\circ$ Sissid–5/2–stip: 90°
Height1
Central density3
Number of pieces62
Related polytopes
ArmySemi-uniform Ipe
RegimentSissiddip
DualGreat dodecahedral tegum
ConjugateGreat dodecahedral prism
Abstract properties
Euler characteristic–8
Topological properties
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The small stellated dodecahedral prism or sissiddip is a prismatic uniform polychoron that consists of 2 small stellated dodecahedra and 12 pentagrammic prisms. Each vertex joins 1 small stellated dodecahedron and 5 pentagrammic prisms. As the name suggests, it is a prism based on the small stellated dodecahedron.

## Vertex coordinates

The vertices of a small stellated dodecahedral prism of edge length 1 are given by all even permutations of the first three coordinates of:

• $\left(0,\,±\frac12,\,±\frac{\sqrt5-1}{4},\,±\frac12\right).$ 