You might also take a look at Slodowy, P. (1983), Platonic Solids, Kleinian Singularities and Lie Groups,Lecture Notes in Mathematics, No. 1008, pp. 102- 138,
Arnold's Trinities paper "Polymathematics : is mathematics a single science or a set of arts?",
easily found on the net
and
Chapoton's own trinities page (also found on the net).
The last two focus on the "E" part of ADE, but give long lists of intriguing parallels.
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