# Pentagrammic duoprism

Pentagrammic duoprism
Rank4
TypeUniform
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${\displaystyle {\sqrt {\frac {5-{\sqrt {5}}}{5}}}\approx 0.74350}$
Inradius${\displaystyle {\sqrt {\frac {5-2{\sqrt {5}}}{20}}}\approx 0.16246}$
Hypervolume${\displaystyle 5{\frac {5-2{\sqrt {5}}}{16}}\approx 0.16496}$
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:

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