Compound of cube and octahedron
This polyhedron 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 and shares the same vertices as a rhombic dodecahedron.
This can be seen as the three-dimensional equivalent of the compound of two squares ; 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:
