A set, not two dice
A domino set holds each pair once: 3-5 is the same tile as 5-3, and it is in the box once. Rolling two dice would make 3-5 twice as likely as 5-5, which is why this draws from the set instead.
Double six has twenty-eight tiles, double nine has fifty-five and double twelve has ninety-one — the triangular numbers, one row per pip count.