# Compound of two hexagonal prisms

Compound of two hexagonal prisms
Rank3
TypeUniform
Notation
Coxeter diagramxo6ox xx
Elements
Components2 hexagonal prisms
Faces12 squares, 4 hexagons as 2 stellated dodecagons
Edges12+24
Vertices24
Vertex figureIsosceles triangle, edge lengths 3, 2, 2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {5}}{2}}\approx 1.11803}$
Volume${\displaystyle 3{\sqrt {3}}\approx 5.19615}$
Dihedral angles4–4: 120°
4–6: 90°
Height1
Central density2
Number of external pieces26
Level of complexity6
Related polytopes
ArmySemi-uniform Twip, edge lengths ${\displaystyle {\frac {{\sqrt {6}}-{\sqrt {2}}}{2}}}$ (base), 1 (sides)
Regiment*
DualCompound of two hexagonal tegums
ConjugateCompound of two hexagonal prisms
Abstract & topological properties
Flag count144
OrientableYes
Properties
SymmetryI2(12)×A1, order 48
ConvexNo
NatureTame

The stellated dodecagonal prism or compound of two hexagonal prisms is a prismatic uniform polyhedron compound. It consists of 2 stellated dodecagons and 12 squares. Each vertex joins one stellated dodecagon and two squares. As the name suggests, it is a prism based on a stellated dodecagon.

Its quotient prismatic equivalent is the hexagonal antiprismatic prism, which is four-dimensional.

## Vertex coordinates

Coordinates for the vertices of a stellated dodecagonal prism of edge length 1 centered at the origin are given by:

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

## Variations

This compound has variants where the bases are non-regular compounds of two hexagons. In these cases the compound has only hexagonal prismatic symmetry and the convex hull is a dihexagonal prism.