# Pentagrammic-octagonal duoprism

The pentagrammic-octagonal duoprism, also known as starodip or the 5/2-8 duoprism, is a uniform duoprism that consists of 8 pentagrammic prisms and 5 octagonal prisms, with 2 of each at each vertex.

Pentagrammic-octagonal duoprism
Rank4
TypeUniform
Notation
Bowers style acronymStarodip
Coxeter diagramx5/2o x8o()
Elements
Cells8 pentagrammic prisms, 5 octagonal prisms
Faces40 squares, 8 pentagrams, 5 octagons
Edges40+40
Vertices40
Vertex figureDigonal disphenoid, edge lengths (5–1)/2 (base 1), 2+2 (base 2), 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {15+5{\sqrt {2}}-{\sqrt {5}}}{10}}}\approx 1.40837}$
Hypervolume${\displaystyle {\frac {\sqrt {75+50{\sqrt {2}}-30{\sqrt {5}}-20{\sqrt {10}}}}{2}}\approx 1.96106}$
Dichoral anglesStip–5/2–stip: 135°
Stip–4–op: 90°
Op–8–op: 36°
Central density2
Number of external pieces18
Level of complexity12
Related polytopes
ArmySemi-uniform podip
RegimentStarodip
DualPentagrammic-octagonal duotegum
ConjugatesPentagonal-octagonal duoprism, Pentagonal-octagrammic duoprism, Pentagrammic-octagrammic duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH2×I2(8), order 160
ConvexNo
NatureTame

## Vertex coordinates

The coordinates of a pentagrammic-octagonal duoprism, centered at the origin and with unit edge length, are given by:

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

## Representations

A pentagrammic-octagonal duoprism has the following Coxeter diagrams: