# Pentagrammic-octagrammic duoprism

Pentagrammic-octagrammic duoprism
Rank4
TypeUniform
Notation
Bowers style acronymStastodip
Coxeter diagramx5/2o x8/3o (         )
Elements
Cells8 pentagrammic prisms, 5 octagrammic prisms
Faces40 squares, 8 pentagrams, 5 octagrams
Edges40+40
Vertices40
Vertex figureDigonal disphenoid, edge lengths (5–1)/2 (base 1), 2–2 (base 2), 2 (sides)
Measures (edge length 1)
Circumradius${\sqrt {\frac {15-5{\sqrt {2}}-{\sqrt {5}}}{10}}}\approx 0.75451$ Dichoral anglesStip–4–stop: 90°
Stip–5/2–stip: 45°
Stop–8/3–stop: 36°
Central density6
Number of external pieces26
Level of complexity24
Related polytopes
ArmySemi-uniform podip
RegimentStastodip
DualPentagrammic-octagrammic duotegum
ConjugatesPentagonal-octagonal duoprism, Pentagonal-octagrammic duoprism, Pentagrammic-octagonal duoprism
Abstract & topological properties
Flag count960
Euler characteristic0
OrientableYes
Properties
SymmetryH2×I2(8), order 160
ConvexNo
NatureTame

The pentagrammic-octagrammic duoprism, also known as stastodip or the 5/2-8/3 duoprism, is a uniform duoprism that consists of 8 pentagrammic prisms and 5 octagrammic prisms, with 2 of each at each vertex.

## Vertex coordinates

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

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

## Representations

A pentagrammic-octagrammic duoprism has the following Coxeter diagrams:

• x5/2o x8/3o (         ) (full symmetry)
• x4/3x x5/2o (         ) (B2×H2 symmetry, octagrams as ditetragrams)