Starting at a corner, could you walk around the surface of this Platonic solid without crossing other corners? To get the answer, you need an 81-holed doughnut. Mathematicians have spent more than 2,000 years dissecting the structure of the five Platonic solids—the tetrahedron, cube, octahedron, icosahedron, and dodecahedron—but there’s still a lot we don’t know …
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