Compound of cube and octahedron

Compound of cube and octahedron
Type	Compound
Stellation core	cuboctahedron
Convex hull	Rhombic dodecahedron
Index	W43
Polyhedra	1 octahedron 1 cube
Faces	8 triangles 6 squares
Edges	24
Vertices	14
Symmetry group	octahedral (Oh)

This polyhedron can be seen as either a polyhedral stellation or a compound.

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.

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:

References

• Wenninger, Magnus (1974). Polyhedron Models. Cambridge University Press. ISBN 978-0-521-09859-5. 

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