Triangular duoprism

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Triangular duoprism
Triangular duoprism.png
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymTriddip
Coxeter diagramx3o x3o (CDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node.png)
Tapertopic notation1111
Elements
Cells6 triangular prisms
Faces6 triangles, 9 squares
Edges18
Vertices9
Vertex figureTetragonal disphenoid, edge lengths 1 (base) and 2 (sides)
Measures (edge length 1)
Circumradius
Inradius
Hypervolume
Dichoral anglesTrip–4–trip: 90°
 Trip–3–trip: 60°
Height
Central density1
Number of pieces6
Level of complexity3
Related polytopes
ArmyTriddip
RegimentTriddip
DualTriangular duotegum
ConjugateNone
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryA2≀S2, order 72
ConvexYes
NatureTame

The triangular duoprism or triddip, also known as the triangular-triangular duoprism, the 3 duoprism or the 3-3 duoprism, is a noble uniform duoprism that consists of 6 triangular prisms, with 4 meeting at each vertex. It is the simplest possible duoprism (excluding the degenerate dichora) and is also the 6-2 gyrochoron. It is the first in an infinite family of isogonal triangular dihedral swirlchora and also the first in an infinite family of isochoric triangular hosohedral swirlchora.

It is also a convex segmentochoron (designated K-4.10 on Richard Klitzing's list), as it is a triangle atop a triangular prism.

Gallery[edit | edit source]

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a triangular duoprism of edge length 1, centered at the origin, are given by:

Representations[edit | edit source]

A triangular duoprism has the following Coxeter diagrams:

  • x3o x3o (full symmetry)
  • ox xx3oo&#x (axial, triangle atop triangular prism)
  • xxoo xoox&#xr (axial, vertex first)
  • xxx3ooo&#x (A2 axial)

Related polychora[edit | edit source]

Isogonal derivatives[edit | edit source]

Substitution by vertices of these following elements will produce these convex isogonal polychora:

External links[edit | edit source]