Hexagonal duoprism
Hexagonal duoprism  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Hiddip 
Coxeter diagram  x6o x6o () 
Elements  
Cells  12 hexagonal prisms 
Faces  36 squares, 12 hexagons 
Edges  72 
Vertices  36 
Vertex figure  Tetragonal disphenoid, edge lengths √3 (base) and √2 (sides) 
Measures (edge length 1)  
Circumradius  
Inradius  
Hypervolume  
Dichoral angles  Hip–6–hip: 120° 
Hip–4–hip: 90°  
Central density  1 
Number of external pieces  12 
Level of complexity  3 
Related polytopes  
Army  Hiddip 
Regiment  Hiddip 
Dual  Hexagonal duotegum 
Conjugate  None 
Abstract & topological properties  
Flag count  864 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  G_{2}≀S_{2}, order 288 
Flag orbits  3 
Convex  Yes 
Nature  Tame 
The hexagonal duoprism or hiddip, also known as the hexagonalhexagonal duoprism, the 6 duoprism or the 66 duoprism, is a noble uniform duoprism that consists of 12 hexagonal prisms, with 4 joining at each vertex. It is also the 125 gyrochoron. It is the first in an infinite family of isogonal hexagonal dihedral swirlchora and also the first in an infinite family of isochoric hexagonal hosohedral swirlchora.
This polychoron can be alternated into a triangular duoantiprism, although it cannot be made uniform.
A unit hexagonal duoprism can be vertexinscribed into the antifrustary distetracontoctachoron and ditetrahedronary dishecatonicosachoron.
Gallery[edit  edit source]

Wireframe, cell, net
Vertex coordinates[edit  edit source]
Coordinates for the vertices of a hexagonal duoprism of edge length 1, centered at the origin, are given by:
 ,
 ,
 ,
 .
Simpler coordinates can be given in 6dimensional space as all permutations of
 ,
where the sum of the first three coordinates is 0. Multiplying these coordinates by gives a set of integral coordinates.
Representations[edit  edit source]
A hexagonal duoprism has the following Coxeter diagrams:
 x6o x6o () (full symmetry)
 x3x x6o () (G_{2}×A_{2} symmetry, one hexagon seen as ditrigon)
 x3x x3x () (A_{2}≀S_{2} symmetry, both hexagons seen as ditrigons)
 xux xxx6ooo&#xt (G_{2}×A_{1} axial)
 xux xxx3xxx&#xt (A_{2}×A_{1} symmetry, ditrigonal axial)
External links[edit  edit source]
 Bowers, Jonathan. "Category A: Duoprisms".
 Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".
 Klitzing, Richard. "hiddip".
 Wikipedia contributors. "66 duoprism".