Triangular-pentagonal duoprism

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Triangular-pentagonal duoprism
Triangular-pentagonal duoprism.png
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymTrapedip
Info
Coxeter diagramx3o x5o
SymmetryA2×H2, order 60
ArmyTrapedip
RegimentTrapedip
Elements
Vertex figureDigonal disphenoid, edge lengths 1 (base 1), (1+5)/2 (base 2), and 2 (sides)
Cells5 triangular prisms, 3 pentagonal prisms
Faces5 triangles, 15 squares, 3 pentagons
Edges15+15
Vertices15
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTrip–3–trip: 108°
 Trip–4–pip: 90°
 Pip–5–pip: 60°
Height
Central density1
Euler characteristic0
Number of pieces8
Level of complexity6
Related polytopes
DualTriangular-pentagonal duotegum
ConjugateTriangular-pentagrammic duoprism
Properties
ConvexYes
OrientableYes
NatureTame

The triangular-pentagonal duoprism or trapedip, also known as the 3-5 duoprism, is a uniform duoprism that consists of 3 pentagonal prisms and 5 triangular prisms, with two of each at each vertex.

It is also a CRF segmentochoron, as pentagon atop pentagonal prism. It is designated K-4.34 on Richard Klitzing's list.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a triangular-pentagonal duoprism with edge length 1 are given by:

Representations[edit | edit source]

A triangular-pentagonal duoprism has the following Coxeter diagrams:

  • x3o x5o (full symmetry)
  • ox xx5oo&#x (pentagon atop pentagon prism)
  • ofx xxx3oooo&#xt (triangle-first)

External links[edit | edit source]