# Pentagonal-octagrammic duoprism

(Redirected from Pistodip)
Pentagonal-octagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymPistodip
Coxeter diagramx5o x8/3o (         )
Elements
Cells8 pentagonal prisms, 5 octagrammic prisms
Faces40 squares, 8 pentagons, 5 octagrams
Edges40+40
Vertices40
Vertex figureDigonal disphenoid, edge lengths (1+5)/2 (base 1), 2–2 (base 2), 2 (sides)
Measures (edge length 1)
Circumradius$\sqrt{\frac{15-5\sqrt2+\sqrt5}{10}} ≈ 1.00822$ Hypervolume$\frac{\sqrt{75-50\sqrt2+30\sqrt5-20\sqrt{10}}}{2} ≈ 8.30720$ Dichoral anglesStop–8/3–stop: 108°
Pip–4–stop: 90°
Pip–5–pip: 45°
Central density3
Number of external pieces21
Level of complexity12
Related polytopes
ArmySemi-uniform podip
RegimentPistodip
DualPentagonal-octagrammic duotegum
ConjugatesPentagonal-octagonal duoprism, Pentagrammic-octagonal duoprism, Pentagrammic-octagrammic duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH2×I2(8), order 160
ConvexNo
NatureTame

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

## Vertex coordinates

The coordinates of a pentagonal-octagrammic duoprism, centered at the origin and with edge length 1, are given by:

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