# Hexagonal duotegum

Hexagonal duotegum
Rank4
TypeNoble
Notation
Bowers style acronymHiddit
Coxeter diagramm6o2m6o ()
Elements
Cells36 tetragonal disphenoids
Faces72 isosceles triangles
Edges12+36
Vertices12
Vertex figureHexagonal tegum
Measures (based on hexagons of edge length 1)
Edge lengthsBase (12): 1
Lacing (36): ${\displaystyle {\sqrt {2}}\approx 1.41421}$
Inradius${\displaystyle {\frac {\sqrt {6}}{4}}\approx 0.61237}$
Central density1
Related polytopes
ArmyHiddit
RegimentHiddit
DualHexagonal duoprism
ConjugateNone
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryG2≀S2, order 288
ConvexYes
NatureTame

The hexagonal duotegum or hiddit, also known as the hexagonal-hexagonal duotegum, the 6 duotegum, or the 6-6 duotegum, is a noble duotegum that consists of 36 tetragonal disphenoids and 12 vertices, with 12 cells joining at each vertex. It is also the 12-5 step prism. It is the first in an infinite family of isogonal hexagonal hosohedral swirlchora and also the first in an infinite family of isochoric hexagonal dihedral swirlchora.

The ratio between the longest and shortest edges is 1:${\displaystyle {\sqrt {2}}}$ ≈ 1:1.41421.

## Vertex coordinates

The vertices of a hexagonal duotegum based on two hexagons of edge length 1, centered at the origin, are given by:

• ${\displaystyle \left(\pm 1,\,0,\,0,\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,0,\,0\right)}$,
• ${\displaystyle \left(0,\,0,\,\pm 1,\,0\right)}$,
• ${\displaystyle \left(0,\,0,\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}}\right)}$.