Above, on the left, is a faceted cuboctahedron. To its right are a faceted snub dodecahedron (upper right) which is also a ten-part compound, and a faceted truncated cube below that. Any of these images may be enlarged by clicking on it.

Below, the left figure is a faceting of the great rhombcuboctahedron — one which is also a three-part compound of octagonal prisms. To its right is a faceting of the snub dodecahedron which is markedly different in appearance from the snub dodecahedron faceting shown above. 

Faceted polyhedra have the same vertices as the polyhedra from which they are derived, but those vertices are connected in different ways, changing the faces and edges.

All of these were made using Stella 4d, a program you may try for yourself, for free, right here.