Polyhedron Compound

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

(1)

or faces of times

(2)

or both

(3)