# compound polyhedron

A compound polyhedron is an assemblage of two or more polyhedra,
usually interpenetrating and having a common center. There are two types:
a combination of a solid with its dual and
an interpenetrating set of several copies of the same polyhedron. The simplest
example of a compound polyhedron is the compound of two tetrahedra,
known as the **stella octangula** and first described by Johannes Kepler. This shape is unique in that it
falls under both of the above classes, because the tetrahedron is the only
self-dual uniform polyhedron;
the edges of the two tetrahedra form the diagonals of the faces of a cube in which the stella octangula can be inscribed. Another example of a compound
follows from an important Platonic relationship: a cube can be inscribed
within a dodecahedron. There are five
different positions for a cube within a dodecahedron; superimposing all
five gives the compound known as the **rhombic triacontahedron**.