A d3 and d12 that, when rolled together, produce the same results as two standard d6!

Many games involve rolling (casting) two six-sided dice together, "2d6" in gamer shorthand. There are 36 possibilities for the result: one each with a sum of 2 or 12 (two 1's or two 6's), two each for 3 or 11, three each for 4 or 10, four each for 5 and 9, five each for 6 and 8, and six for 7. There are also 36 possibilities for rolling a d3 with a d12. The d3 in our specially-designed pair is numbered 1, 2, and 3, but the d12 is numbered 1, 2, 3, 4, 4, 5, 5, 6, 6, 7, 8, and 9. The distribution of the results is identical to that of two standard d6.