Compound of cube and octahedron
# Compound of cube and octahedron

Compound of cube and octahedron :

| Type | Compound |
| - | - |
| Coxeter diagram | ∪ |
| Stellation core | cuboctahedron |
| Convex hull | Rhombic dodecahedron |
| Index | $W_{43}$ |
| Polyhedra | 1 octahedron 1 cube |
| Faces | 8 triangles 6 squares |
| Edges | 24 |
| Vertices | 14 |
| Symmetry group | octahedral $(O_h)$ |

The compound of cube and octahedron is a polyhedron which can be seen as either a polyhedral stellation or a compound.

## Construction

The 14 Cartesian coordinates of the vertices of the compound are.

    6: (±2, 0, 0), ( 0, ±2, 0), ( 0, 0, ±2)
    8: ( ±1, ±1, ±1)

## As a compound

It can be seen as the compound of an octahedron and a cube. It is one of four compounds constructed from a Platonic solid or Kepler-Poinsot polyhedron and its dual.

It has octahedral symmetry $(O_h)$ and shares the same vertices as a rhombic dodecahedron.

This can be seen as the three-dimensional equivalent of the compound of two squares ({8/2} "octagram"); this series continues on to infinity, with the four-dimensional equivalent being the compound of tesseract and 16-cell.

| A cube and its dual octahedron | The intersection of both solids is the cuboctahedron, and their convex hull is the rhombic dodecahedron. |
| - | - |

## As a stellation

It is also the first stellation of the cuboctahedron and given as Wenninger model index 43.

It can be seen as a cuboctahedron with square and triangular pyramids added to each face.

The stellation facets for construction are:

