So why are these the only (regular) dice you'll ever see?

The video explains why only five Platonic solids exist, using both geometric and topological proofs. The geometric explanation involves folding regular polygons to form 3D shapes, while the topological proof uses Euler's characteristic to demonstrate the constraints on polyhedra. The video also discusses why other shapes cannot form additional Platonic solids.

What new insight or understanding did you gain from this video?

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