# Hendecagonal-tetrahedral duoprism

Hendecagonal-tetrahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymHentet
Coxeter diagramx11o x3o3o
Elements
Tera11 tetrahedral prisms, 4 triangular-hendecagonal duoprisms
Cells11 tetrahedra, 44 triangular prisms, 6 hendecagonal prisms
Faces44 triangles, 66 squares, 4 hendecagons
Edges44+66
Vertices44
Vertex figureTriangular scalene, edge lengths 1 (base triangle), 2cos(π/11) (top), 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {{\frac {3}{8}}+{\frac {1}{4\sin ^{2}{\frac {\pi }{11}}}}}}\approx 1.87741}$
Hypervolume${\displaystyle {\frac {11{\sqrt {2}}}{48\tan {\frac {\pi }{11}}}}\approx 1.10375}$
Diteral anglesTepe–tet–tepe: ${\displaystyle {\frac {9\pi }{11}}\approx 147.27273^{\circ }}$
Tepe–trip–thendip: 90°
Thendip–henp–thendip: ${\displaystyle \arccos {\left({\frac {1}{3}}\right)}\approx 70.52878^{\circ }}$
HeightsHeng atop thendip: ${\displaystyle {\frac {\sqrt {6}}{3}}\approx 0.81650}$
Henp atop perp henp: ${\displaystyle {\frac {\sqrt {2}}{2}}\approx 0.70711}$
Central density1
Number of external pieces15
Level of complexity10
Related polytopes
ArmyHentet
RegimentHentet
DualHendecagonal-tetrahedral duotegum
ConjugatesSmall hendecagrammic-tetrahedral duoprism, Hendecagrammic-tetrahedral duoprism, Great hendecagrammic-tetrahedral duoprism, Grand hendecagrammic-tetrahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryA3×I2(11), order 528
ConvexYes
NatureTame

The hendecagonal-tetrahedral duoprism or hentet is a convex uniform duoprism that consists of 11 tetrahedral prisms and 4 triangular-hendecagonal duoprisms. Each vertex joins 2 tetrahedral prisms and 3 triangular-hendecagonal duoprisms.

## Vertex coordinates

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

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

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