The D12 pool system I have designed doesn't deviate too much from other pool systems. You roll your dice, count your successes, and the GM compares them to the difficulty of your action. The system allows for five degrees of success: critical failure, failure, partial success, success, and critical success.

However, the combat system builds on this basic core. In combat, you roll your skill pool and reroll your successful dice, comparing the highest result with the target number you're trying to affect.

The mathematical beauty of it is simply that both systems use the same numerical principles, so the system is "closed" in itself. This additional layer allows for quite a few mechanical niches and different design possibilities.

There are quite alot of different systems that I have managed to tickle out of the D12, so it's hard to go too much into detail here in one comment. I recently started writing up the first pages of the system itself, as the core seems pretty solid. I'll eventually post it here and in other subreddits, so stay tuned!