A polyhedron compound is an arrangement of a number of interpenetrating polyhedra, either all the same or of several distinct types, usually having visually attractive
symmetric properties. Compounds of multiple Platonic and Archimedean solids can be
especially attractive, as can compounds of these solids and their duals. For example,
the compound of the tetrahedron and its dual gives
a tetrahedron 2-compound whose hull is
known as the stella octangula.

Particularly nice compounds are produced by rotating copies of a regular solid with -gonal
faces about axes from the origin through the center of each face by an angle of radians. Such compounds are illustrated
above for the Platonic solids and Kepler-Poinsot
polyhedra

Other attractive compounds can be obtained by rotating copies of a solid about a rotational axis by for , ..., .

While there is no standard notation for polyhedral compounds, in Coxeter's notation,
distinct polyhedron vertices of taken times are denoted

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