Triangular-heptagonal duoprismatic prism

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Triangular-heptagonal duoprismatic prism
Rank5
TypeUniform
Notation
Bowers style acronymTrahep
Coxeter diagramx x3o x7o ()
Elements
Tera7 triangular-square duoprisms, 2 triangular-heptagonal duoprisms, 3 square-heptagonal duoprisms
Cells7+14 triangular prisms, 21 cubes, 3+6 heptagonal prisms
Faces14 triangles, 21+21+42 squares, 6 heptagons
Edges21+42+42
Vertices42
Vertex figureDigonal disphenoidal pyramid, edge lengths 1 (disphenoid base 1), 2cos(π/7) (disphenoid base 2), 2 (remaining edges)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTisdip–trip–tisdip:
 Theddip–trip–tisdip: 90°
 Squahedip–cube–tisdip: 90°
 Theddip–hep–squahedip: 90°
 Squahedip–hep–squahedip: 60°
HeightsTheddip atop theddip: 1
 Hep atop squahedip:
Central density1
Number of external pieces12
Level of complexity30
Related polytopes
ArmyTrahep
RegimentTrahep
DualTriangular-heptagonal duotegmatic tegum
ConjugatesTriangular-heptagrammic duoprismatic prism, Triangular-great heptagrammic duoprismatic prism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryA2×I2(7)×A1, order 168
ConvexYes
NatureTame

The triangular-heptagonal duoprismatic prism or trahep, also known as the triangular-heptagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 triangular-heptagonal duoprisms, 3 square-heptagonal duoprisms, and 7 triangular-square duoprisms. Each vertex joins 2 triangular-square duoprisms, 2 square-heptagonal duoprisms, and 1 triangular-heptagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

Vertex coordinates[edit | edit source]

The vertices of a triangular-heptagonal duoprismatic prism of edge length 2sin(π/7) are given by:

where j = 2, 4, 6.

Representations[edit | edit source]

A triangular-heptagonal duoprismatic prism has the following Coxeter diagrams:

  • x x3o x7o (full symmetry)
  • xx3oo xx7oo&#x (triangular-heptagonal duoprism atop triangular-heptagonal duoprism)
  • ox xx xx7oo&#x (heptagonal prism atop square-heptagonal duoprism)