Hexagonal-tetrahedral duoprism

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Hexagonal-tetrahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymHatet
Coxeter diagramx6o x3o3o ()
Elements
Tera6 tetrahedral prisms, 4 triangular-hexagonal duoprisms
Cells6 tetrahedra, 24 triangular prisms, 6 hexagonal prisms
Faces24 triangles, 36 squares, 4 hexagons
Edges24+36
Vertices24
Vertex figureTriangular scalene, edge lengths 1 (base triangle), 3 (top), 2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTepe–tet–tepe: 120°
 Tepe–trip–thiddip: 90°
 Thiddip–hip–thiddip:
HeightsHig atop thiddip:
 Hip atop perp hip:
Central density1
Number of external pieces10
Level of complexity10
Related polytopes
ArmyHatet
RegimentHatet
DualHexagonal-tetrahedral duotegum
ConjugateNone
Abstract & topological properties
Flag count2880
Euler characteristic2
OrientableYes
Properties
SymmetryA3×G2, order 288
ConvexYes
NatureTame

The hexagonal-tetrahedral duoprism or hatet is a convex uniform duoprism that consists of 6 tetrahedral prisms and 4 triangular-hexagonal duoprisms. Each vertex joins 2 tetrahedral prisms and 3 triangular-hexagonal duoprisms.

Vertex coordinates[edit | edit source]

The vertices of a hexagonal-tetrahedral duoprism of edge length 1 are given by all even sign changes of the last three coordinates of:

Representations[edit | edit source]

A hexagonal-tetrahedral duoprism has the following Coxeter diagrams:

  • x6o x3o3o (full symmetry)
  • x3x x3o3o (hexagons as ditrigons)
  • ox3oo xx6oo&#x (hexagon atop triangular-hexagonal duoprism)
  • ox3oo xx3xx&#x
  • ox xo xx6oo&#x (hexagonal prism atop orthogonal hexagonal prism)
  • ox xo xx3xx&#x
  • oox xxx3xxx&#x
  • xxxx3xxxx&#x

External links[edit | edit source]