An octahedron whose faces are connected only at certain vertices can be opened and rotated. Halfway through the rotation, an outline of a cuboctahedron is formed; at the end of the rotation it closes up into another octahedron.
Halfway through the transformation (t=0.5, Snapshot 2), the edges form a cuboctahedron.
The parameterization of the coordinates was inspired by an actual physical model, several meters in diameter, constructed for the "Heureka" science fair in Zurich in 1991. It was first derived by Roman E. Maeder for: R. E. Maeder, Informatik für Mathematiker und Naturwissenschaftler, Bonn: Addison-Wesley, 1993.