Compound of cube and octahedron

Compound of cube and octahedron
TypeCompound
Coxeter diagram
Stellation corecuboctahedron
Convex hullRhombic dodecahedron
IndexW43
Polyhedra1 octahedron
1 cube
Faces8 triangles
6 squares
Edges24
Vertices14
Symmetry groupoctahedral (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 (Oh) 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

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