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The compound of five octahedra is one of the five regular polyhedron compounds. This polyhedron can be seen as either a polyhedral stellation or a compound. This compound was first described by Edmund Hess in 1876.
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As a stellation
It is the second stellation of the icosahedron, and given as Wenninger model index 23.
It can be constructed by a rhombic triacontahedron with rhombic-based pyramids added to all the faces, as shown by the five colored model image. (This construction does not generate the regular compound of five octahedra, but shares the same topology and can be smoothly deformed into the regular compound.)
As a compound
It can also be seen as a polyhedral compound of five octahedra arranged in icosahedral symmetry (Ih).
It shares its edges and half of its triangular faces with the compound of five tetrahemihexahedra.
As a facetting
It is also a faceting of an icosidodecahedron, shown at left.