# Hexagonal duoprism

Hexagonal duoprism Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymHiddip
Coxeter diagramx6o x6o (       )
Elements
Cells12 hexagonal prisms
Faces36 squares, 12 hexagons
Edges72
Vertices36
Vertex figureTetragonal disphenoid, edge lengths 3 (base) and 2 (sides)
Measures (edge length 1)
Circumradius$\sqrt2 ≈ 1.41421$ Inradius$\frac{\sqrt3}{2} ≈ 0.86603$ Hypervolume$\frac{27}{4} = 6.75$ Dichoral anglesHip–6–hip: 120°
Hip–4–hip: 90°
Central density1
Number of external pieces12
Level of complexity3
Related polytopes
ArmyHiddip
RegimentHiddip
DualHexagonal duotegum
ConjugateNone
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryG2≀S2, order 288
ConvexYes
NatureTame

The hexagonal duoprism or hiddip, also known as the hexagonal-hexagonal duoprism, the 6 duoprism or the 6-6 duoprism, is a noble uniform duoprism that consists of 12 hexagonal prisms, with 4 joining at each vertex. It is also the 12-5 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 vertex-inscribed into the antifrustary distetracontoctachoron and ditetrahedronary dishecatonicosachoron.

## Vertex coordinates

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

• $\left(0,\,±1,\,0,\,±1\right),$ • $\left(0,\,±1,\,±\frac{\sqrt3}{2},\,±\frac12\right),$ • $\left(±\frac{\sqrt3}{2},\,±\frac12,\,0,\,±1\right),$ • $\left(±\frac{\sqrt3}{2},\,±\frac12,\,±\frac{\sqrt3}{2},\,±\frac12\right).$ ## Representations

A hexagonal duoprism has the following Coxeter diagrams:

• x6o x6o (full symmetry)
• x3x x6o (one hexagon seen as ditrigon)
• x3x x3x (both hexagons seen as ditrigons, triangular duoprismatic symmetry)
• xux xxx6ooo&#xt (hexagonal axial)
• xux xxx3xxx&#xt (ditrigonal axial)