Hendecagonal-truncated tetrahedral duoprism Rank 5 Type Uniform Notation Bowers style acronym Hentut Coxeter diagram x11o x3x3o Elements Tera 4 triangular-hendecagonal duoprisms , 11 truncated tetrahedral prisms , 4 hexagonal-hendecagonal duoprisms Cells 44 triangular prisms , 44 hexagonal prisms , 11 truncated tetrahedra , 6+12 hendecagonal prisms Faces 44 triangles , 66+132 squares , 44 hexagons , 12 hendecagons Edges 66+132+132 Vertices 132 Vertex figure Digonal disphenoidal pyramid , edge lengths 1, √3 , √3 (base triangle), 2cos(π/11) (top), √2 (side edges)Measures (edge length 1) Circumradius ${\sqrt {{\frac {11}{8}}+{\frac {1}{4\sin ^{2}{\frac {\pi }{11}}}}}}\approx 2.12713$ Hypervolume ${\frac {253{\sqrt {2}}}{48\tan {\frac {\pi }{11}}}}\approx 25.38628$ Diteral angles Tuttip–tut–tuttip: ${\frac {9\pi }{11}}\approx 147.27273^{\circ }$ Thendip-henp-hahendip: $\arccos \left(-{\frac {1}{3}}\right)\approx 109.47122^{\circ }$ Thendip–trip–tuttip: 90° Hahendip-hip-tuttip: 90° Hahendip–henp–hahendip: $\arccos \left({\frac {1}{3}}\right)\approx 70.52877^{\circ }$ Central density 1 Number of external pieces 19 Level of complexity 30 Related polytopes Army Hentut Regiment Hentut Dual Hendecagonal-triakis tetrahedral duotegum Conjugates Small hendecagrammic-truncated tetrahedral duoprism , Hendecagrammic-truncated tetrahedral duoprism , Great hendecagrammic-truncated tetrahedral duoprism , Grand hendecagrammic-truncated tetrahedral duoprism Abstract & topological properties Euler characteristic 2 Orientable Yes Properties Symmetry A_{3} ×I2(11) , order 528Convex Yes Nature Tame

The hendecagonal-truncated tetrahedral duoprism or hentut is a convex uniform duoprism that consists of 11 truncated tetrahedral prisms , 4 hexagonal-hendecagonal duoprisms , and 4 triangular-hendecagonal duoprisms . Each vertex joins 2 truncated tetrahedral prisms, 1 triangular-hendecagonal duoprism, and 2 hexagonal-hendecagonal duoprisms.

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

$\left(1,\,0,\,{\frac {3{\sqrt {2}}\sin {\frac {\pi }{11}}}{2}},\,{\frac {{\sqrt {2}}\sin {\frac {\pi }{11}}}{2}},\,{\frac {{\sqrt {2}}\sin {\frac {\pi }{11}}}{2}}\right),$
$\left(\cos \left({\frac {j\pi }{11}}\right),\,\pm \sin \left({\frac {j\pi }{11}}\right),\,{\frac {3{\sqrt {2}}\sin {\frac {\pi }{11}}}{2}},\,{\frac {{\sqrt {2}}\sin {\frac {\pi }{11}}}{2}},\,{\frac {{\sqrt {2}}\sin {\frac {\pi }{11}}}{2}}\right),$
where j = 2, 4, 6, 8, 10.