Hendecagonal-tetrahedral duoprism

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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
Hypervolume
Diteral anglesTepe–tet–tepe:
 Tepe–trip–thendip: 90°
 Thendip–henp–thendip:
HeightsHeng atop thendip:
 Henp atop perp henp:
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[edit | edit source]

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:

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