# Hendecagonal-truncated tetrahedral duoprism

Hendecagonal-truncated tetrahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymHentut
Coxeter diagramx11o x3x3o
Elements
Tera4 triangular-hendecagonal duoprisms, 11 truncated tetrahedral prisms, 4 hexagonal-hendecagonal duoprisms
Cells44 triangular prisms, 44 hexagonal prisms, 11 truncated tetrahedra, 6+12 hendecagonal prisms
Faces44 triangles, 66+132 squares, 44 hexagons, 12 hendecagons
Edges66+132+132
Vertices132
Vertex figureDigonal disphenoidal pyramid, edge lengths 1, 3, 3 (base triangle), 2cos(π/11) (top), 2 (side edges)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {{\frac {11}{8}}+{\frac {1}{4\sin ^{2}{\frac {\pi }{11}}}}}}\approx 2.12713}$
Hypervolume${\displaystyle {\frac {253{\sqrt {2}}}{48\tan {\frac {\pi }{11}}}}\approx 25.38628}$
Diteral anglesTuttip–tut–tuttip: ${\displaystyle {\frac {9\pi }{11}}\approx 147.27273^{\circ }}$
Thendip-henp-hahendip: ${\displaystyle \arccos \left(-{\frac {1}{3}}\right)\approx 109.47122^{\circ }}$
Thendip–trip–tuttip: 90°
Hahendip-hip-tuttip: 90°
Hahendip–henp–hahendip: ${\displaystyle \arccos \left({\frac {1}{3}}\right)\approx 70.52877^{\circ }}$
Central density1
Number of external pieces19
Level of complexity30
Related polytopes
ArmyHentut
RegimentHentut
DualHendecagonal-triakis tetrahedral duotegum
ConjugatesSmall hendecagrammic-truncated tetrahedral duoprism, Hendecagrammic-truncated tetrahedral duoprism, Great hendecagrammic-truncated tetrahedral duoprism, Grand hendecagrammic-truncated tetrahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryA3×I2(11), order 528
ConvexYes
NatureTame

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.

## Vertex coordinates

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:

• ${\displaystyle \left(1,\,0,\,{\frac {3{\sqrt {2}}\sin {\frac {\pi }{11}}}{2}},\,{\frac {{\sqrt {2}}\sin {\frac {\pi }{11}}}{2}},\,{\frac {{\sqrt {2}}\sin {\frac {\pi }{11}}}{2}}\right),}$
• ${\displaystyle \left(\cos \left({\frac {j\pi }{11}}\right),\,\pm \sin \left({\frac {j\pi }{11}}\right),\,{\frac {3{\sqrt {2}}\sin {\frac {\pi }{11}}}{2}},\,{\frac {{\sqrt {2}}\sin {\frac {\pi }{11}}}{2}},\,{\frac {{\sqrt {2}}\sin {\frac {\pi }{11}}}{2}}\right),}$

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