Dissection of a Cube into a Cuboctahedron and an Octahedron

truncation

step 1

step 2

step 3

separate

show point numbering

opacity 1

opacity 2

With the truncation slider all the way to the right, this Demonstration gives a dissection of a cube into a cuboctahedron and an octahedron. For other settings, the dissection gives a truncated cube and an octahedron.