Small stellated dodecahedral prism

Small stellated dodecahedral prism
Rank4
TypeUniform
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${\displaystyle {\sqrt {\frac {7-{\sqrt {5}}}{8}}}\approx 0.77168}$
Hypervolume${\displaystyle {\frac {3{\sqrt {5}}-5}{4}}\approx 0.42705}$
Dichoral anglesStip–4–stip: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }}$
Sissid–5/2–stip: 90°
Height1
Central density3
Number of external pieces62
Related polytopes
ArmySemi-uniform Ipe
RegimentSissiddip
DualGreat dodecahedral tegum
ConjugateGreat dodecahedral prism
Abstract & topological properties
Euler characteristic–8
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:

• ${\displaystyle \left(0,\,\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {1}{2}}\right).}$