Hendecagonaltruncated cubic duoprism 


Rank  5 

Type  Uniform 

Notation 

Bowers style acronym  Hentic 

Coxeter diagram  x11o x4x3o 

Elements 

Tera  8 triangularhendecagonal duoprisms, 11 truncated cubic prisms, 6 octagonalhendecagonal duoprisms 

Cells  88 triangular prisms, 66 octagonal prisms, 12+24 hendecagonal prisms, 11[truncated cubic prism]]s 

Faces  88 triangles, 132+264 squares, 66 octagons, 24 hendecagons 

Edges  132+264+264 

Vertices  264 

Vertex figure  Digonal disphenoidal pyramid, edge lengths 1, √2+√2, √2+√2 (base triangle), 2cos(π/11) (top), √2 (side edges) 

Measures (edge length 1) 

Circumradius  ${\frac {\sqrt {7+4{\sqrt {2}}+{\frac {1}{\sin ^{2}{\frac {\pi }{11}}}}}}{2}}\approx 2.51275$ 

Hypervolume  ${\frac {77(3+2{\sqrt {2}})}{12\tan {\frac {\pi }{11}}}}\approx 127.36955$ 

Diteral angles  Ticcup–tic–ticcup: ${\frac {9\pi }{11}}\approx 147.27273^{\circ }$ 

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

 Thendip–trip–ticcup: 90° 

 Ohendip–op–ticcup: 90° 

 Ohendip–henp–ohendip: 90° 

Central density  1 

Number of external pieces  25 

Level of complexity  30 

Related polytopes 

Army  Hentic 

Regiment  Hentic 

Dual  Hendecagonaltriakis octahedral duotegum 

Conjugates  Small hendecagrammictruncated cubic duoprism, Hendecagrammictruncated cubic duoprism, Great hendecagrammictruncated cubic duoprism, Grand hendecagrammictruncated cubic duoprism, Hendecagonalquasitruncated hexahedral duoprism, Small hendecagrammicquasitruncated hexahedral duoprism, Hendecagrammicquasitruncated hexahedral duoprism, Great hendecagrammicquasitruncated hexahedral duoprism, Grand hendecagrammicquasitruncated hexahedral duoprism 

Abstract & topological properties 

Euler characteristic  2 

Orientable  Yes 

Properties 

Symmetry  B_{3}×I2(11), order 1056 

Convex  Yes 

Nature  Tame 

The hendecagonaltruncated cubic duoprism or hentic is a convex uniform duoprism that consists of 11 truncated cubic prisms, 6 octagonalhendecagonal duoprisms, and 8 triangularhendecagonal duoprisms. Each vertex joins 2 truncated cubic prisms, 1 triangularhendecagonal duoprism, and 2 octagonalhendecagonal duoprisms.
The vertices of a hendecagonaltruncated cubic duoprism of edge length 2sin(π/11) are given by all permutations of the last three coordinates of:
 $\left(1,\,0,\,\pm (1+{\sqrt {2}})\sin {\frac {\pi }{11}},\,\pm (1+{\sqrt {2}})\sin {\frac {\pi }{11}},\,\pm \sin {\frac {\pi }{11}}\right),$
 $\left(\cos \left({\frac {j\pi }{11}}\right),\,\pm \sin \left({\frac {j\pi }{11}}\right),\,\pm (1+{\sqrt {2}})\sin {\frac {\pi }{11}},\,\pm (1+{\sqrt {2}})\sin {\frac {\pi }{11}},\,\pm \sin {\frac {\pi }{11}}\right),$
where j = 2, 4, 6, 8, 10.