Triangular duoprismatic prism

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Triangular duoprismatic prism
Rank5
TypeUniform
Notation
Bowers style acronymTratrip
Coxeter diagramx x3o x3o ()
Tapertopic notation11111
Elements
Tera2 triangular duoprisms, 6 triangular-square duoprisms
Cells6+12 triangular prisms, 9 cubes
Faces12 triangles, 18+18 squares
Edges9+36
Vertices18
Vertex figureTetragonal disphenoidal pyramid, edge lengths 1 (disphenoid bases) and 2 (remaining edges)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTriddip–trip–tisdip: 90º
 Tisdip–cube–tisdip: 90º
 Tisdip–trip–tisdip: 60º
HeightsTriddip atop triddip: 1
 Trip atop tisdip: 3/2 \approx 0.86603
Central density1
Number of external pieces8
Level of complexity15
Related polytopes
ArmyTratrip
RegimentTratrip
DualTriangular duotegmatic tegum
ConjugateTriangular duoprismatic prism
Abstract & topological properties
Flag count2160
Euler characteristic2
OrientableYes
Properties
SymmetryA2≀S2×A1, order 144
ConvexYes
NatureTame

The triangular duoprismatic prism or tratrip, also known as the triangular-triangular prismatic duoprism, is a convex uniform duoprism that consists of 2 triangular duoprisms and 6 triangular-square duoprisms. Each vertex joins 1 triangular duoprism and 4 triangular-square duoprisms. As the name suggests, it is a prism based on the triangular duoprism, which also makes it a convex segmentoteron.

Vertex coordinates[edit | edit source]

The vertices of a triangular duoprismatic prism of edge length 1 are given by:

Representations[edit | edit source]

A triangular duoprismatic prism has the following Coxeter diagrams:

  • x x3o x3o (full symmetry)
  • xx3oo xx3oo&#x (A2×A2 symmetry)
  • ox xx xx3oo&#x (A2×A1×A1 symmetry, triangular prism atop triangular-square duoprism)
  • xxx xxx3ooo&#x (A2×A1 symmetry, three different triangular prisms)

External links[edit | edit source]