Books can be written about the finite subgroups of $\mathrm{SL}(2,\mathbb C)$ (and their immediate family, like the polyhedral groups...) I am about to start writing notes for a short course about them and I would like to include references to as much useful and interesting information about them as possible. Since they show up in quite different contexts, and can be looked upon from many different points of view, I am sure the very varied MO audience knows lots of things about them I don't.
So, despite this being more or less canonically too broad/vague a question for MO according to the FAQ:
Can you tell me (or at least point me to) all about the finite subgroups of $\mathrm{SL}(2,\mathbb C)$?
LATER: Thanks to everyone who answered. So far, the information is essentially of algebraic and geometric nature. I wonder now about combinatorics and such beasts.
For example, it is a theorem of Whitney (or maybe it just follows easily from a theorem of Whitney) that a 3-connected simple planar graph with $e$ edges has an automorphism group of order at most $4e$, and that the order is $4e$ precisely when the graph comes from a polyhedron, so that the group is a polyhedral group.
Do you know of similar results?
