Why are there just five platonic solids (and what are platonic solids!?) More links & stuff in full description below ↓↓↓ The solids are the tetrahedron, hexahedron (cube), octahedron, icosahedron and dodecahedron. Featuring Katie Steckles and James Grime - https://twitter.com/stecks and https://twitter.com/jamesgrime Our thanks to the kind people at Polydron for giving Katie some pentagons - http://www.polydron.com/ NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: http://www.patreon.com/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Numberphile T-Shirts: null Other merchandise: https://store.dftba.com/collections/numberphile