LS has a post up about using 1d12 to determine weather randomly. That’s a cool idea (I do something similar by making weather a sort of reaction roll with the cosmos, which I may have gotten originally from Talysman).
But I don’t want to talk about weather here, I want to talk about using 1d12 as a general resolution system. It has a reasonably large set of possibilities, and is also quite pleasant to roll. As LS points out, though 1d12 is not as common in the real world as 2d6, it does have the advantage of not requiring any addition. So how does it stack up for a five-fold result space? (All percentile probabilities are rounded, and so may not sum to 100%.)
Neither of the 1d12 possibilities matches up exactly, and bonuses affect the result slightly differently than with 2d6, but it’s probably “good enough” to use with the same kind of probability curve (not quite a bell curve, but a big middle with small tails). I prefer the LS distribution; the alternate is just presented for comparison.
For a “1d12 only” game, you could use ability modifiers rather than full stats, and all action resolution could be done using the 1d12 simulation of 2d6 fivefold results. Rather than 3d6 in order, there would be 1d12 in order…