# Hendecagonal-truncated octahedral duoprism

Hendecagonal-truncated octahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymHentoe
Coxeter diagramx11o o4x3x ()
Elements
Tera6 square-hendecagonal duoprisms, 11 truncated octahedral prisms, 8 hexagonal-hendecagonal duoprisms
Cells66 cubes, 88 hexagonal prisms, 12+24 hendecagonal prisms, 11 truncated octahedra
Faces66+132+264 squares, 88 hexagons, 24 hendecagons
Edges132+264+264
Vertices264
Vertex figureDigonal disphenoidal pyramid, edge lengths 2, 3, 3 (base triangle), 2cos(π/11) (top), 2 (side edges)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {10+{\frac {1}{\sin ^{2}{\frac {\pi }{11}}}}}}{2}}\approx 2.37690}$
Hypervolume${\displaystyle {\frac {22{\sqrt {2}}}{\tan {\frac {\pi }{11}}}}\approx 105.96012}$
Diteral anglesTope–toe–tope: ${\displaystyle {\frac {9\pi }{11}}\approx 147.27273^{\circ }}$
Shendip–henp–hahendip: ${\displaystyle \arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }}$
Hahendip–henp–hahendip: ${\displaystyle \arccos \left(-{\frac {1}{3}}\right)\approx 109.47122^{\circ }}$
Shendip–cube–tope: 90°
Hahendip–hip–tope: 90°
Central density1
Number of external pieces25
Level of complexity30
Related polytopes
ArmyHentoe
RegimentHentoe
DualHendecagonal-tetrakis hexahedral duotegum
ConjugatesSmall hendecagrammic-truncated octahedral duoprism, Hendecagrammic-truncated octahedral duoprism, Great hendecagrammic-truncated octahedral duoprism, Grand hendecagrammic-truncated octahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB3×I2(11), order 1056
ConvexYes
NatureTame

The hendecagonal-truncated octahedral duoprism or hentoe is a convex uniform duoprism that consists of 11 truncated octahedral prisms, 8 hexagonal-hendecagonal duoprisms, and 6 square-hendecagonal duoprisms. Each vertex joins 2 truncated octahedral prisms, 1 square-hendecagonal duoprism, and 2 hexagonal-hendecagonal duoprisms.

## Vertex coordinates

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

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

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

## Representations

A hendecagonal-truncated octahedral duoprism has the following Coxeter diagrams:

• x11o o4x3x (full symmetry)
• x11o x3x3x ()