algorithmic modeling for Rhino
Most regular polyhedrons are based on either tetrahedral and/or octahedral or icosahedral geometry. Therefore they can be reduced by using their symmetry planes. Being cut out of three mirrors, the piece remaining is enough to display the initial volume. This video shows how most of the platonic, archimedian and catalan solids are displayed with these three types of kaleidoscopes. On the lower left you see the unrolled version of the kaleidoscope. Only very small variations are necessary.
Some polyhedrons in those groups are not being displayed, because they are based on rotational symmetry (e.g. Snubcube).