Triangular-rectified pentachoric duoprism

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Triangular-rectified pentachoric duoprism
Rank6
TypeUniform
Notation
Bowers style acronymTrarap
Coxeter diagramx3o o3x3o3o ()
Elements
Peta5 triangular-tetrahedral duoprisms, 5 triangular-octahedral duoprisms, 3 rectified pentachoric prisms
Tera15 tetrahedral prisms, 10+20 triangular duoprisms, 15 octahedral prisms, 3 rectified pentachora
Cells15 tetrahedra, 30+30+60 triangular prisms, 15 octahedra
Faces10+30+60 triangles, 90 squares
Edges30+90
Vertices30
Vertex figureTriangular prismatic scalene, edge lengths 1 (base tetrahedron and top edge) and 2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dipetal anglesTratet–triddip–troct:
 Rappip–ope–troct: 90°
 Rappip–tepe–tratet: 90°
 Troct–triddip–troct:
 Rappip–rap–rappip: 60°
HeightsRap atop rappip:
 Tratet atop troctt:
Central density1
Number of external pieces13
Level of complexity45
Related polytopes
ArmyTrarap
RegimentTrarap
DualTriangular-joined pentachoric duotegum
ConjugateNone
Abstract & topological properties
Flag count32400
Euler characteristic0
OrientableYes
Properties
SymmetryA4×A2, order 720
ConvexYes
NatureTame

The triangular-rectified pentachoric duoprism or trarap is a convex uniform duoprism that consists of 3 rectified pentachoric prisms, 5 triangular-octahedral duoprisms, and 5 triangular-tetrahedral duoprisms. Each vertex joins 2 rectified pentachoric prisms, 2 triangular-tetrahedral duoprisms, and 3 triangular-octahedral duoprisms. It is a duoprism based on a triangle and a rectified pentachoron, and is thus also a convex segmentopeton, as a rectified pentachoron atop rectified pentachoric prism.

Vertex coordinates[edit | edit source]

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

  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • .

Representations[edit | edit source]

A triangular-rectified pentachoric duoprism has the following Coxeter diagrams:

  • x3o o3x3o3o () (full symmetry)
  • xx3oo xo3ox3oo&#x (A3×A2 symmetry, triangular-tetrahedral duoprism atop triangular-octahedral duoprism)
  • ox oo3xx3oo3oo&#x (A4×A1 symmetry, rectified pentachoron atop rectified pentachoric prism)

External links[edit | edit source]