# Great stellated dodecahedral prism

The great stellated dodecahedral prism or gissiddip is a prismatic uniform polychoron that consists of 2 great stellated dodecahedra and 12 pentagrammic prisms. Each vertex joins 1 great stellated dodecahedron and 3 pentagrammic prisms. As the name suggests, it is a prism based on the great stellated dodecahedron.

Great stellated dodecahedral prism
Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGissiddip
Coxeter diagramx x5/2o3o ()
Elements
Cells12 pentagrammic prisms, 2 great stellated dodecahedra
Faces30 squares, 24 pentagrams
Edges20+60
Vertices40
Vertex figureTriangular pyramid, edge lengths (5–1)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{11-3\sqrt5}{8}} ≈ 0.73244}$
Hypervolume${\displaystyle \frac{7\sqrt5-15}{4} ≈ 0.16312}$
Dichoral anglesGissid–5/2–stip: 90°
Stip–4–stip: ${\displaystyle \arccos\left(\frac{\sqrt5}{5}\right) ≈ 63.43495^\circ}$
Height1
Central density7
Number of external pieces62
Related polytopes
ArmySemi-uniform Dope
RegimentGissiddip
DualGreat icosahedral tegum
ConjugateDodecahedral prism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

## Vertex coordinates

The vertices of a great stellated dodecahedral prism of edge length 1 are given by:

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

along with all even permutations of:

• ${\displaystyle \left(±\frac{3+\sqrt5}{4},\,±\frac12,\,0,\,±\frac12\right).}$