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.

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: