32 and Truncated Icosahedron
The 32-sided truncated icosahedron forms the basis of many footballs (soccer balls!). It's also a big deal in chemistry.
sixtysymbols video on footballs: http://www.youtube.com/watch?v=55M1cq62m2c
periodicvideos video on buckyballs: http://www.youtube.com/watch?v=ljF5QhD5hnI
This video featured Dr James Grime at Nottingham Forest's stadium, The City Ground.