GEK1518 Mathematics in Art and Architecture, 2003/04 II, Tutorial 4

  1. Why there are only five Platonic solids? Compare it with the proof that there are only three Platonic tilings of the plane.
  2. 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