# Hendecagonal-octahedral duoprism

Hendecagonal-octahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymHenoct
Coxeter diagramx11o o4o3x
Elements
Tera11 octahedral prisms, 8 triangular-hendecagonal duoprisms
Cells88 triangular prisms, 11 octahedra, 12 hendecagonal prisms
Faces88 triangles, 132 squares, 88 hendecagons
Edges66+132
Vertices66
Vertex figureSquare scalene, edge lengths 1 (base square), 2cos(π/11) (top), 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {2+{\frac {1}{\sin ^{2}{\frac {\pi }{11}}}}}}{2}}\approx 1.91041}$
Hypervolume${\displaystyle {\frac {11{\sqrt {2}}}{12\tan {\frac {\pi }{11}}}}\approx 4.41500}$
Diteral anglesOpe–oct–ope: ${\displaystyle {\frac {9\pi }{11}}\approx 147.27273^{\circ }}$
Thendip–henp–thendip: ${\displaystyle \arccos \left(-{\frac {1}{3}}\right)\approx 109.47122^{\circ }}$
Thendip–trip–ope: 90°
Height${\displaystyle {\frac {\sqrt {6}}{3}}\approx 0.81650}$
Central density1
Number of external pieces19
Level of complexity10
Related polytopes
ArmyHenoct
RegimentHenoct
DualHendecagonal-cubic duotegum
ConjugatesSmall hendecagrammic-octahedral duoprism, Hendecagrammic-octahedral duoprism, Great hendecagrammic-octahedral duoprism, Grand hendecagrammic-octahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB3×I2(11), order 1056
ConvexYes
NatureTame

The hendecagonal-octahedral duoprism or henoct is a convex uniform duoprism that consists of 11 octahedral prisms and 8 triangular-hendecagonal duoprisms. Each vertex joins 2 octahedral prisms and 4 triangular-hendecagonal duoprisms.

## Vertex coordinates

The vertices of a hendecagonal-octahedral duoprism of edge length 2sin(π/11) are given by all permutations and sign changes of the last three coordinates of:

• ${\displaystyle \left(1,\,0,\,0,\,0,\,{\sqrt {2}}\sin {\frac {\pi }{11}}\right),}$
• ${\displaystyle \left(\cos \left({\frac {j\pi }{11}}\right),\,\pm \sin \left({\frac {j\pi }{11}}\right),\,0,\,0,\,{\sqrt {2}}\sin {\frac {\pi }{11}}\right),}$

where j = 2, 4, 6, 8, 10.