# Octagonal-hexagonal antiprismatic duoprism

Octagonal-hexagonal antiprismatic duoprism
Rank5
TypeUniform
Notation
Bowers style acronymOhap
Coxeter diagramx8o s2s12o
Elements
Tera8 hexagonal antiprismatic prisms, 12 triangular-octagonal duoprisms, 2 hexagonal-octagonal duoprisms
Cells96 triangular prisms, 16 hexagonal prisms, 8 hexagonal antiprisms, 12+12 octagonal prisms
Faces96 triangles, 96+96 squares, 16 hexagons, 12 octagons
Edges96+96+96
Vertices96
Vertex figureIsosceles-trapezoidal scalene, edge lengths 1, 1, 1, 3 (base trapezoid), 2+2 (top), 2 (side edges)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {7+2{\sqrt {2}}+{\sqrt {3}}}}{2}}\approx 1.70004}$
Hypervolume${\displaystyle 2{\sqrt {6+4{\sqrt {2}}+6{\sqrt {3}}+4{\sqrt {6}}}}\approx 11.28665}$
Diteral anglesTodip–op–todip: = ${\displaystyle \arccos \left({\frac {1-2{\sqrt {3}}}{3}}\right)\approx 145.22189^{\circ }}$
Happip–hap–happip: 135°
Todip–op–hodip: = ${\displaystyle \arccos \left({\frac {3-2{\sqrt {3}}}{3}}\right)\approx 98.89943^{\circ }}$
Todip–trip–happip: 90°
Hodip–hip–happip: 90°
Height${\displaystyle {\sqrt {{\sqrt {3}}-1}}\approx 0.85560}$
Central density1
Number of external pieces22
Level of complexity40
Related polytopes
ArmyOhap
RegimentOhap
DualOctagonal-hexagonal antitegmatic duotegum
ConjugateOctagrammic-hexagonal antiprismatic duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryI2(8)×I2(12)×A1+, order 384
ConvexYes
NatureTame

The octagonal-hexagonal antiprismatic duoprism or ohap is a convex uniform duoprism that consists of 8 hexagonal antiprismatic prisms, 2 hexagonal-octagonal duoprisms, and 12 triangular-octagonal duoprisms. Each vertex joins 2 hexagonal antiprismatic prisms, 3 triangular-octagonal duoprisms, and 1 hexagonal-octagonal duoprism.

## Vertex coordinates

The vertices of an octagonal-hexagonal antiprismatic duoprism of edge length 1 are given by all permutations of the first two coordinates of:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,{\frac {\sqrt {{\sqrt {3}}-1}}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm 1,\,0,\,{\frac {\sqrt {{\sqrt {3}}-1}}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {1}{2}},\,-{\frac {\sqrt {{\sqrt {3}}-1}}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,0,\,\pm 1,\,-{\frac {\sqrt {{\sqrt {3}}-1}}{2}}\right).}$

## Representations

An octagonal-hexagonal antiprismatic duoprism has the following Coxeter diagrams:

• x8o s2s12o (full symmetry; hexagonal antiprisms as alternated dodecagonal prisms)
• x8o s2s6s (hexagonal antiprisms as alternated dihexagonal prisms)
• x4x s2s12o (octagons as ditetragons)
• x4x s2s6s