There’s a certain beauty in the inevitability of the 5 Platonic solids – we can say with certainty that they are all of the possible regular tilings of the sphere, and that they are the only possibilities.

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There are also many neat and beautiful relationships between them (such as the dualities, the space filling packing of cubes, or of tetrahedra and octahedra).
So far, so tidy, but let’s take a look at the tetrahedron. Take 2 and join them face to face…take another and join it so they all share an edge…then another…and another…you are back to the beginning – full circle…almost!

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