# Pentagrammic duoprism

Pentagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymStardip
Coxeter diagramx5/2o x5/2o ()
Elements
Cells10 pentagrammic prisms
Faces25 squares, 10 pentagrams
Edges50
Vertices25
Vertex figureTetragonal disphenoid, edge lengths (5–1)/2 (bases) and 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{5-\sqrt5}{5}} ≈ 0.74350}$
Inradius${\displaystyle \sqrt{\frac{5-2\sqrt5}{20}} ≈ 0.16246}$
Hypervolume${\displaystyle 5\frac{5-2\sqrt5}{16} ≈ 0.16496}$
Dichoral anglesStip–4–stip: 90°
Stip–5/2-stip: 36°
Central density4
Number of external pieces20
Level of complexity12
Related polytopes
ArmyPedip
RegimentStardip
DualPentagrammic duotegum
ConjugatePentagonal duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH2≀S2, order 200
ConvexNo
NatureTame

The pentagrammic duoprism or stardip, also known as the pentagrammic-pentagrammic duoprism, the 5/2 duoprism or the 5/2-5/2 duoprism, is a noble uniform duoprism that consists of 10 pentagrammic prisms, with 4 meeting at each vertex.

## Vertex coordinates

The coordinates of a pentagrammic duoprism of edge length 1, centered at the origin, are given by:

• ${\displaystyle \left(±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}}\right),}$
• ${\displaystyle \left(±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}}\right),}$
• ${\displaystyle \left(±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,0,\,-\sqrt{\frac{5-\sqrt5}{10}}\right),}$
• ${\displaystyle \left(±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}},\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}}\right),}$
• ${\displaystyle \left(±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}},\,±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}}\right),}$
• ${\displaystyle \left(±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}},\,0,\,-\sqrt{\frac{5-\sqrt5}{10}}\right),}$
• ${\displaystyle \left(0,\,-\sqrt{\frac{5-\sqrt5}{10}},\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}}\right),}$
• ${\displaystyle \left(0,\,-\sqrt{\frac{5-\sqrt5}{10}},\,±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}}\right),}$
• ${\displaystyle \left(0,\,-\sqrt{\frac{5-\sqrt5}{10}},\,0,\,-\sqrt{\frac{5-\sqrt5}{10}}\right).}$