Hendecagonaltruncated octahedral duoprism 


Rank  5 

Type  Uniform 

Notation 

Bowers style acronym  Hentoe 

Coxeter diagram  x11o o4x3x () 

Elements 

Tera  6 squarehendecagonal duoprisms, 11 truncated octahedral prisms, 8 hexagonalhendecagonal duoprisms 

Cells  66 cubes, 88 hexagonal prisms, 12+24 hendecagonal prisms, 11 truncated octahedra 

Faces  66+132+264 squares, 88 hexagons, 24 hendecagons 

Edges  132+264+264 

Vertices  264 

Vertex figure  Digonal disphenoidal pyramid, edge lengths √2, √3, √3 (base triangle), 2cos(π/11) (top), √2 (side edges) 

Measures (edge length 1) 

Circumradius  ${\frac {\sqrt {10+{\frac {1}{\sin ^{2}{\frac {\pi }{11}}}}}}{2}}\approx 2.37690$ 

Hypervolume  ${\frac {22{\sqrt {2}}}{\tan {\frac {\pi }{11}}}}\approx 105.96012$ 

Diteral angles  Tope–toe–tope: ${\frac {9\pi }{11}}\approx 147.27273^{\circ }$ 

 Shendip–henp–hahendip: $\arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }$ 

 Hahendip–henp–hahendip: $\arccos \left({\frac {1}{3}}\right)\approx 109.47122^{\circ }$ 

 Shendip–cube–tope: 90° 

 Hahendip–hip–tope: 90° 

Central density  1 

Number of external pieces  25 

Level of complexity  30 

Related polytopes 

Army  Hentoe 

Regiment  Hentoe 

Dual  Hendecagonaltetrakis hexahedral duotegum 

Conjugates  Small hendecagrammictruncated octahedral duoprism, Hendecagrammictruncated octahedral duoprism, Great hendecagrammictruncated octahedral duoprism, Grand hendecagrammictruncated octahedral duoprism 

Abstract & topological properties 

Euler characteristic  2 

Orientable  Yes 

Properties 

Symmetry  B_{3}×I_{2}(11), order 1056 

Convex  Yes 

Nature  Tame 

The hendecagonaltruncated octahedral duoprism or hentoe is a convex uniform duoprism that consists of 11 truncated octahedral prisms, 8 hexagonalhendecagonal duoprisms, and 6 squarehendecagonal duoprisms. Each vertex joins 2 truncated octahedral prisms, 1 squarehendecagonal duoprism, and 2 hexagonalhendecagonal duoprisms.
The vertices of a hendecagonaltruncated octahedral duoprism of edge length 2sin(π/11) are given by all permutations of the last three coordinates of:
 $\left(1,\,0,\,0,\,\pm {\sqrt {2}}\sin {\frac {\pi }{11}},\,\pm 2{\sqrt {2}}\sin {\frac {\pi }{11}}\right),$
 $\left(\cos \left({\frac {j\pi }{11}}\right),\,\pm \sin \left({\frac {j\pi }{11}}\right),\,0,\,\pm {\sqrt {2}}\sin {\frac {\pi }{11}},\,\pm 2{\sqrt {2}}\sin {\frac {\pi }{11}}\right),$
where j = 2, 4, 6, 8, 10.
A hendecagonaltruncated octahedral duoprism has the following Coxeter diagrams:
 x11o o4x3x (full symmetry)
 x11o x3x3x ()