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}) 
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.
 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 KeplerPoinsot 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 threedimensional equivalent of the compound of two squares ({8/2} "octagram"); this series continues on to infinity, with the fourdimensional equivalent being the compound of tesseract and 16cell.

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:
See also
 Compound of two tetrahedra
 Compound of dodecahedron and icosahedron
 Compound of small stellated dodecahedron and great dodecahedron
 Compound of great stellated dodecahedron and great icosahedron
References
 Wenninger, Magnus (1974). Polyhedron Models. Cambridge University Press. ISBN 9780521098595.
This polyhedronrelated article is a stub. You can help Wikipedia by expanding it. 