Diophantine equations, Platonic solids, McKay correspondence, equivelar maps and Vogel's universality

H. M. Khudaverdian, R. L. Mkrtchyan

We notice that one of the Diophantine equations, $knm=2kn+2km+2nm$, arising in the universality originated Diophantine classification of simple Lie algebras, has interesting interp…