Construction Based on Kepler's Mysterium Cosmographicum

show rhombic hexecontahedron

perforate

show rhombic triaontahedron

perforate

uncheck the boxes above to perforate the Platonic solids:

dodecahedron

cuboid

tetrahedron

octahedron

Inspired by Kepler's Mysterium Cosmographicum, this Demonstration shows a nesting of the Platonic solids, the rhombic triaontahedron and rhombic hexecontahedron.