# Rectified hexagonal duoprism

Rectified hexagonal duoprism
Rank4
TypeIsogonal
Notation
Bowers style acronymRehiddip
Elements
Cells36 tetragonal disphenoids, 12 rectified hexagonal prisms
Faces144 isosceles triangles, 36 squares, 12 hexagons
Edges72+144
Vertices72
Vertex figureWedge
Measures (based on hexagons of edge length 1)
Edge lengthsLacing edges (144): ${\displaystyle {\frac {\sqrt {6}}{3}}\approx 0.81650}$
Edges of base hexagons (72): 1
Circumradius${\displaystyle {\frac {\sqrt {21}}{3}}\approx 1.52753}$
Central density1
Related polytopes
ArmyRehiddip
RegimentRehiddip
DualJoined hexagonal duotegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryG2≀S2, order 288
ConvexYes
NatureTame

The rectified hexagonal duoprism or rehiddip is a convex isogonal polychoron that consists of 12 rectified hexagonal prisms and 36 tetragonal disphenoids. 3 rectified hexagonal prisms and 2 tetragonal disphenoids join at each vertex. It can be formed by rectifying the hexagonal duoprism.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform hexagonal duoprisms, where the edges of one hexagon are ${\displaystyle {\frac {2{\sqrt {3}}}{3}}\approx 1.15470}$ times as long as the edges of the other.

The ratio between the longest and shortest edges is 1:${\displaystyle {\frac {\sqrt {6}}{2}}}$ ≈ 1:1.22474.

## Vertex coordinates

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

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