Truncating the Platonic solids to create the Archimedean solids

     Symmetrically truncating the vertices of the regular Platonic solids creates most

of the semi-regular Archimedean solids.  This permits the symmetry of the latter to

be associated with the former in a straightforward manner.  For example the cube

and octahedron can be progressively truncated to yield the cuboctahedron. The

Fig. 13 -   Truncating the cube and octahedron to make the cuboctahedron

truncated cube and the truncated octahedron are generated in the process.  Since

each vertex of the polyhedra are symmetrically sliced off the resulting polyhedra

retain the same symmetry elements as the original. 

Exercise: Truncating the vertices of  which polyhedron produces the triangle

faces of the cuboctahedron?  Which one produces the square's?  Why?

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