Two pairs of dice with the same probability

Question

Alice has two dice each numbered from 1 to 6.
Bob has two dice as well, the numbering is not known, but each face has a positive integer. The numbering on each dice can be different and a number can appear more than once on a dice.

Alice rolls her two dice and the probability for each of the numbers 2, 3, 4, .., 12 as the total of the two dice is the same for Bob, if he rolls his two dice.

Is this only possible if Bob has the same numbering as Alice on his two dice?

Answer 1

No, Bob could have a pair of Sicherman Dice

Sicherman dice /ˈsɪkərmən/ are the only pair of 6-sided dice that are not normal dice, bear only positive integers, and have the same probability distribution for the sum as normal dice. They were invented in 1978 by George Sicherman of Buffalo, New York.

Their face values are: 1–2–2–3–3–4, and 1–3–4–5–6–8.