Cube and Octahedron to Cuboctahedron

Drag the applet to the extreme right and observe what happens. Note: It seems that GeoGebra has a bug. It's not displaying correctly. I'll try to see if I can fix this.
The corners of cube and an octahedron are cut off until the new faces share vertices. Both transformations result in a solid with 6 square faces and 8 triangular faces. This new solid is called cuboctahedron.