Triangular duoprism
Triangular duoprism  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Triddip 
Coxeter diagram  x3o x3o () 
Tapertopic notation  1^{1}1^{1} 
Elements  
Cells  6 triangular prisms 
Faces  6 triangles, 9 squares 
Edges  18 
Vertices  9 
Vertex figure  Tetragonal disphenoid, edge lengths 1 (base) and √2 (sides) 
Measures (edge length 1)  
Circumradius  
Inradius  
Hypervolume  
Dichoral angles  Trip–4–trip: 90° 
Trip–3–trip: 60°  
Height  
Central density  1 
Number of external pieces  6 
Level of complexity  3 
Related polytopes  
Army  Triddip 
Regiment  Triddip 
Dual  Triangular duotegum 
Conjugate  None 
Abstract & topological properties  
Flag count  216 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  A_{2}≀S_{2}, order 72 
Flag orbits  3 
Convex  Yes 
Nature  Tame 
The triangular duoprism or triddip, also known as the triangulartriangular duoprism, the 3 duoprism or the 33 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 62 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 K4.10 on Richard Klitzing's list), as it is a triangle atop a triangular prism.
Gallery[edit  edit source]

Segmentochoron display, triangle atop triangular prism

Wireframe, cell, net
Vertex coordinates[edit  edit source]
Coordinates for the vertices of a triangular duoprism of edge length 1, centered at the origin, are given by:
 ,
 ,
 ,
 .
Simpler coordinates can be given in 6dimensions, as all permutations of
 ,
where the sum of the first 3 coordinates is equal to the sum of the last 3.
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 (A_{2} axial)
Related polychora[edit  edit source]
Isogonal derivatives[edit  edit source]
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 Triangular prism (6): Triangular duotegum
 Triangle (6): Triangular duotegum
 Square (9): Triangular duoprism
 Edge (18): Rectified triangular duoprism
External links[edit  edit source]
 Bowers, Jonathan. "Category A: Duoprisms".
 Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".
 Klitzing, Richard. "triddip".
 Quickfur. "The 3,3Duoprism".
 Wikipedia contributors. "33 duoprism".
 Hi.gher.Space Wiki Contributors. "Duotrianglinder".