The first animations truncate a regular polyhedron to the mid-points
of its edges, then switch to the dual model and truncate back
from the mid-points of its edges.
The second animations show the full range of an idealised truncation.
The edges are treated as lines rather than line segments. The edges
are cut in a ratio that ranges from -infinity to +infinity.
At the
extremes of the range the circumsphere of the model grows to become
infinitely large. In order to view the transformation the truncated model
is scaled to maintain the circumsphere at a constant size. The effect on
the base polyhedron is to shrink it into the centre at the
extreme ratios.
The animations were made with the following scripts
