Relabelled die making sums 1 to 12 uniform

You have a standard die numbered $1$ to $6$ and a second fair six-sided die whose faces carry unknown numbers (not necessarily $1$ to $6$). Rolling both, every total from $1$ to $12$ is equally likely. What do the faces of the second die add up to?

18. Twelve equally likely totals over $36$ outcomes means each total occurs $3$ times. A total of $1$ needs a $0$ on the mystery die three times, and a total of $12$ needs a $6$ three times, so the faces are $0,0,0,6,6,6$, summing to $18$.