- Why there are only five Platonic solids? Compare it with the proof that there are only three Platonic tilings of the plane.
- The cube and the octahedron are dual, and midpoint-truncation of either will give the cuboctahedron. In the same way, the dodecahedron and the icosahedron are dual, and midpoint-truncation of either will give the icosidodecahedron. What do you get if you do a midpoint-truncation of the tetrahedron?

Helmer Aslaksen

Department of Mathematics

National University of Singapore

helmer.aslaksen@gmail.com