The alternating group of degree 5 and the icosahedron rotations: seeing   not only proving
  When compared with pure mathematicians, applied ones have a clear preference for proofs that go beyond a chain of reasonings and do exhibit the fact to be proved. Here we exhibit the bijection between the 60 icosahedron rotations of the group R and the 60 permutations of the group A5. 
J. M. S. Sim\~oes-Pereira
math.HO