# Octagonal-octahedral duoprism

Octagonal-octahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymOwoct
Coxeter diagramx8o o4o3x ()
Elements
Tera8 octahedral prisms, 8 triangular-octagonal duoprisms
Cells64 triangular prisms, 8 octahedra, 12 octagonal prisms
Faces64 triangles, 96 squares, 6 octagons
Edges48+96
Vertices48
Vertex figureSquare scalene, edge lengths 1 (base square), 2+2 (top), 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {3+{\sqrt {2}}}{2}}}\approx 1.48563}$
Hypervolume${\displaystyle {\frac {4+2{\sqrt {2}}}{3}}\approx 2.27614}$
Diteral anglesOpe–oct–ope: 135°
Todip–op–todip: ${\displaystyle \arccos \left(-{\frac {1}{3}}\right)\approx 109.47122^{\circ }}$
Todip–trip–ope: 90°
${\displaystyle {\frac {\sqrt {6}}{3}}\approx 0.81650}$
Central density1
Number of external pieces16
Level of complexity10
Related polytopes
ArmyOwoct
RegimentOwoct
DualOctagonal-cubic duotegum
ConjugateOctagrammic-octahedral duoprism
Abstract & topological properties
Flag count7680
Euler characteristic2
OrientableYes
Properties
SymmetryB3×I2(8), order 768
ConvexYes
NatureTame

The octagonal-octahedral duoprism or owoct is a convex uniform duoprism that consists of 8 octahedral prisms and 8 triangular-octagonal duoprisms. Each vertex joins 2 octahedral prisms and 4 triangular-octagonal duoprisms.

## Vertex coordinates

The vertices of an octagonal-octahedral duoprism of edge length 1 are given by all permutations and sign changes of the last three coordinates of:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,0,\,0,\,{\frac {\sqrt {2}}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,{\frac {\sqrt {2}}{2}}\right)}$.

## Representations

An octagonal-octahedral duoprism has the following Coxeter diagrams:

• x8o o4o3x () (full symmetry)
• x4x o4o3x () (octagons as ditetragons)
• x8o o3x3o () (octahedra as tetratetrahedra)
• x4x o3x3o () (octagons as ditetragons and octahedra as tetratetrahedra)
• xo3ox xx8oo&#x (triangular-octagonal duoprism atop triangle-gyrated triangular-octagonal duoprism)