Truncation is the removal of portions of solids falling outside a set of symmetrically placed planes.
The operation implemented as Truncate[polyhedron, r] in the Wolfram Language
package PolyhedronOperations` displaces points along the edges of a polyhedron
by a ratio 
,
where 
is the fraction of the edge length at
which to truncate, and then fills in the resulting holes with new polygons. While
this is not true truncation, the operation is equivalent to truncation for regular
solids and 
.
The operation is implemented in the Wolfram
Language as TruncatedPolyhedron[poly].
The dual operation of truncation is augmentation, which is the operation of replacing facial polygons with pyramids.
As illustrated above, 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).
Furthermore, seven of the 13 Archimedean solids can be constructed from Platonic solids by truncation, which the four remaining Archimedeans requiring either expansion or snubification.
