# Pentagrammic-octagonal duoprism

(Redirected from Starodip)
Pentagrammic-octagonal duoprism
Rank4
TypeUniform
SpaceSpherical
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$\sqrt{\frac{15+5\sqrt2-\sqrt5}{10}} ≈ 1.40837$ Hypervolume$\frac{\sqrt{75+50\sqrt2-30\sqrt5-20\sqrt{10}}}{2} ≈ 1.96106$ 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

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.

## Vertex coordinates

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

• $\left(±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,±\frac12,\,±\frac{1+\sqrt2}2\right),$ • $\left(±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,±\frac{1+\sqrt2}2,\,±\frac12\right),$ • $\left(±\frac{\sqrt5-1}4,\,\sqrt{\frac{5+\sqrt5}{40}},\,±\frac12,\,±\frac{1+\sqrt2}2\right),$ • $\left(±\frac{\sqrt5-1}4,\,\sqrt{\frac{5+\sqrt5}{40}},\,±\frac{1+\sqrt2}2,\,±\frac12\right),$ • $\left(0,\,-\sqrt{\frac{5-\sqrt5}{10}},\,±\frac12,\,±\frac{1+\sqrt2}2\right),$ • $\left(0,\,-\sqrt{\frac{5-\sqrt5}{10}},\,±\frac{1+\sqrt2}2,\,±\frac12\right).$ ## Representations

A pentagrammic-octagonal duoprism has the following Coxeter diagrams:

• x5/2o x8o (full symmetry)
• x4x x5/2o (       ) (BC2×H2 symmetry, octagons as ditetragons)