# Triangular duoprism

Triangular duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymTriddip
Coxeter diagramx3o x3o ()
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${\displaystyle \frac{\sqrt6}{3} ≈ 0.81650}$
Inradius${\displaystyle \frac{\sqrt3}{6} ≈ 0.28868}$
Hypervolume${\displaystyle \frac{3}{16} = 0.1875}$
Dichoral anglesTrip–4–trip: 90°
Trip–3–trip: 60°
Height${\displaystyle \frac{\sqrt3}{2} ≈ 0.86603}$
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.

## Vertex coordinates

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

• ${\displaystyle \left(0,\,\frac{\sqrt3}{3},\,0,\,\frac{\sqrt3}{3}\right),}$
• ${\displaystyle \left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,-\frac{\sqrt3}{6}\right),}$
• ${\displaystyle \left(±\frac12,\,-\frac{\sqrt3}{6},\,0,\,\frac{\sqrt3}{3}\right),}$
• ${\displaystyle \left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,-\frac{\sqrt3}{6}\right).}$

## Representations

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

### Isogonal derivatives

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