# Octagonal-decagonal duoprism

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Octagonal-decagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymOdedip
Info
Coxeter diagramx8o x10o
SymmetryI2(8)×I2(10), order 320
ArmyOdedip
RegimentOdedip
Elements
Vertex figureDigonal disphenoid, edge lengths 2+2 (base 1), (5+5)/2 (base 2), and 2 (sides)
Cells10 octagonal prisms, 8 decagonal prisms
Faces80 squares, 10 octagons, 8 decagons
Edges80+80
Vertices80
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{5+\sqrt2+\sqrt5}{2}} ≈ 2.07970}$
Hypervolume${\displaystyle 5\sqrt{15+10\sqrt2+6\sqrt5+4\sqrt{10}} ≈ 37.15093}$
Dichoral anglesOp–8–op: 144°
Dip–10–dip: 135°
Dip–4–op: 90°
Central density1
Euler characteristic0
Number of pieces18
Level of complexity6
Related polytopes
DualOctagonal-decagonal duotegum
ConjugatesOctagonal-decagrammic duoprism, Octagrammic-decagonal duoprism, Octagrammic-decagrammic duoprism
Properties
ConvexYes
OrientableYes
NatureTame

The octagonal-decagonal duoprism or odedip, also known as the 8-10 duoprism, is a uniform duoprism that consists of 8 decagonal prisms and 10 octagonal prisms, with two of each joining at each vertex.

This polychoron can be alternated into a square-pentagonal duoantiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a pentagonal-square prismantiprismoid, which is also nonuniform.

## Vertex coordinates

The vertices of an octagonal-decagonal duoprism of edge length 1, centered at the origin, are given by:

• ${\displaystyle \left(±\frac12,\,±\frac{1+\sqrt2}{2},\,0,\,±\frac{1+\sqrt5}{2}\right),}$
• ${\displaystyle \left(±\frac12,\,±\frac{1+\sqrt2}{2},\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4}\right),}$
• ${\displaystyle \left(±\frac12,\,±\frac{1+\sqrt2}{2},\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12\right),}$
• ${\displaystyle \left(±\frac{1+\sqrt2}{2},\,±\frac12,\,0,\,±\frac{1+\sqrt5}{2}\right),}$
• ${\displaystyle \left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4}\right),}$
• ${\displaystyle \left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12\right).}$

## Representations

An octagonal-decagonal duoprism has the following Coxeter diagrams:

• x8o x10o (full symmetry)
• x5x x10o (octagons as ditetragons0
• x5x x8o (decagons as dipentagons)
• x4x x5x (both of these applied)