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Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).

2 votes

Classification of Platonic solids

I believe Hermann Weyl's classic book 'Symmetry' discusses this question but I can't recall what his approach is (ie, whether he makes use of the Euler formula).
George Melvin's user avatar