There are many ways a platonic solid fits elegantly inside another platonic solid, both duals and non-duals.
And you can make them all pump!

Image 3.04: pumping tetrahedron and octahedron; and their intersecting volume

On the right: the morphing intersection volume of a tetrahedron and octahedron. It moves from octahedron to truncated tetrahedron (archimedean) to tetrahedron.

Image 3.03: pumping cube and tetrahedron

Image 3.02: spinning and pumping cube and icosahedron

Image 3.01: pumping cube and dodecahedron