Compound of cube and octahedron

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 (Oh) 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.

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:
 * [[Image:First stellation of cuboctahedron trifacets.png|240px]][[Image:First stellation of cuboctahedron square facets.png|240px]]