Truncation

The removal of portions of Solids falling outside a set of symmetrically placed planes. The five Platonic Solids belong to one of the following three truncation series (which, in the first two cases, carry the solid to its Dual Polyhedron).

$\begin{figure}\begin{center}\BoxedEPSF{TruncationCube.epsf scaled 1200}\end{center}\end{figure}$

$\begin{figure}\begin{center}\BoxedEPSF{TruncationIcosahedron.epsf scaled 1200}\end{center}\end{figure}$

$\begin{figure}\begin{center}\BoxedEPSF{TruncationTetrahedron.epsf scaled 1200}\end{center}\end{figure}$