There are exactly 5 regular convex polyhedra (Euclid's Elements XIII): the tetrahedron {3,3}, octahedron {3,4}, icosahedron {3,5}, cube {4,3}, and dodecahedron {5,3}. Proof via Schläfli symbol and the angular deficit bound (p−2)(q−2) < 4,…
There are exactly 5 regular convex polyhedra (Euclid's Elements XIII): the tetrahedron {3,3}, octahedron {3,4}, icosahedron {3,5}, cube {4,3}, and dodecahedron {5,3}. Proof via Schläfli symbol and the angular deficit bound (p−2)(q−2) < 4,…