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 known as the stella octangula.

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

(1)

or faces of times

(2)

or both

(3)

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Weisstein, Eric W. "Polyhedron Compound." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PolyhedronCompound.html