Poor cube got left out 
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These are very special to physics, chemistry, and biology. One example showing this is Johann Kepler’s Mysterium Cosmographicum which relates these geometries to the orbits of the planets within our star systempic.twitter.com/OS03Ts5qi7
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There are stunning models of these in the Leonardo Museum in Vinci. http://museoleonardiano.it/eng/museum/exhibition-route …pic.twitter.com/TQvFqzA3jP
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I designed and printed T-shirts a couple of years ago incorporating some of those drawings. I still have several in stock: https://mathartfun.com/PolyhedraShirts.html …pic.twitter.com/PzkLiRFx5a
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Amazing, is the fullerene shape a kind of Platonic solid?
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Nope, a requirement for being a platonic solid is to have all faces be the same regular polygon. A fullerene has hexagons and pentagons
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For those interested, this is from "De Divina Proportione" by Luca Pacioli - in collaboration with Da Vinci (1509)
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This is from the Libellus of Luca Pacioli? Leonardo may have done those drawings, but I'm pretty sure there's no explicit attribution. And the book is a translation of a work done 30 years earlier by Piero della Francesca (also uncredited). But I agree they're gorgeous.
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DaVinci just wanted to play some Dungeons and Dragons
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