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See detailOn pairs of commuting involutions in $ Sym(n)$ and $ Alt(n)$
Kiefer, Ann UL; Leemans, Dimitri

in Communications in Algebra (2013), 41(12), 4408--4418

The number of pairs of commuting involutions in Sym(n) and Alt(n) is determined up to isomorphism. It is also proven that, up to isomor- phism and duality, there are exactly two abstract regular polyhedra ... [more ▼]

The number of pairs of commuting involutions in Sym(n) and Alt(n) is determined up to isomorphism. It is also proven that, up to isomor- phism and duality, there are exactly two abstract regular polyhedra on which the group Sym(6) acts as a regular automorphism group. [less ▲]

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