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Think of any vertex. It can't connect to itself, nor the two neighboring vertices already connected by edges, but that still leaves 9 vertices to connect to.
12 vertices each connected to 9 other vertices would seem to imply 108 diagonals... except you are double-counting everything (a diagonal from A to B is the same as a diagonal from B to A). So divide this number by 2.
Note: The general formula for the number of diagonals in an n-gon is:
n(n-3) / 2