Desert Island Math, May 2, 2022 (Polyhedra)

Please visit MoMath’s link which contains some my videos. You may find the “Jump-In Geometry” series to be worth visiting.

In case you are curious, here is the T-shirt design for the difficult icosahedron/dodecahdron problem from the 2005 Bay Area Mathematical Olympiad.

To learn about polyhedra, you have to build them. Polyhedral Models by Wenninger is an excellent book.
You should also buy some zometools. Additionally, you may want to play with a virtual zometools platform like vzome, but you must build physical models to build your intuition.

Coxeter’s classic Regular Polytopes is advanced, but worth looking at. It’s beautifully written.

Here are several books recommended by audience members:

  • Shaping Space, ed. M. Senechal, Springer
  • Shapes, Space, and Symmetry, by A. Holden
  • The Platonic Solids Activity Book, A. Fetter et al., Key Curriculum
  • M. C. Escher Kaleidocycles, D. Schattschneider & W. Walker, Taschen
  • Euler’s Gem: The Polyhedron Formula and The Birth of Topology by David S. Richeson

I’ve used a number of GeoGebra files to produce today’s program, and am sharing my dodecahedronand icosahedron files.