Here we see how a cube may fit inside a dodecahedron. There are five
ways to fit the cube in, which gives us the familiar
compound of 5 cubes. On the other hand, there
are two ways to fit a dodecahedron around a given cube, which leads to
a compound of two dodecahedra. Taking the first stellation of each
gives this compound of two small stellated dodecahedra.