Triangular-cubic duoprism

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Triangular-cubic duoprism
Rank5
TypeUniform
Notation
Bowers style acronymTracube
Coxeter diagramx3o x4o3o ()
Tapertopic notation11111
Elements
Tera6 triangular-square duoprisms, 3 tesseracts
Cells12 triangular prisms, 3+18 cubes
Faces8 triangles, 18+36 squares
Edges24+36
Vertices24
Vertex figureTriangular scalene, edge lengths 1 (top), 2 (base triangle and sides)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTes–cube–tisdip: 90°
 Tisdip–trip–tisdip: 90°
 Tes–cube–tes: 60°
HeightsTisdip atop tisdip: 1
 Cube atop tes:
Central density1
Number of external pieces9
Level of complexity10
Related polytopes
ArmyTracube
RegimentTracube
DualTriangular-octahedral duotegum
ConjugateNone
Abstract & topological properties
Flag count2880
Euler characteristic2
OrientableYes
Properties
SymmetryB3×A2, order 288
ConvexYes
NatureTame

The triangular-cubic duoprism or tracube, also known as a triangular-square duoprismatic prism, is a convex uniform duoprism that consists of 3 tesseracts and 6 triangular-square duoprisms. Each vertex joins 2 tesseracts and 3 triangular-square duoprisms. It is a duoprism based on a triangle and a cube, which makes it a convex segmentoteron, and it can also be viewed as a duoprism based on a square and a triangular prism.

Vertex coordinates[edit | edit source]

The vertices of a triangular-cubic duoprism of edge length 1 are given by:

Representations[edit | edit source]

A triangular-cubic duoprism has the following Coxeter diagrams:

  • x3o x4o3o (full symmetry)
  • x x3o x4o (triangular-square duoprismatic prism)
  • x x x x3o (triangular prismatic prismatic prism)
  • xx3oo xx4oo&#x (triangular-square duoprism atop triangular-square duoprism)
  • xx3oo xx xx&#x
  • ox xx xx4oo&#x (cube atop tesseract)
  • ox xx xx xx&#x
  • xxx xxx xxx&#x

External links[edit | edit source]