Platonic solids generate their four-dimensional analogues

Platonic solids are regular bodies in three dimensions, such as the cube and icosahedron, and have been known for millennia. They feature prominently in the natural world wherever geometry and symmetry are important, for instance in lattices and quasi-crystals, as well as fullerenes and viruses. Platonic solids have counterparts in four dimensions, and mathematicians have now shown that there are six of them, five of which have very strange symmetries.

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