dice – Where is this six-sided die?

This may not be related to role-playing games. I'm going to try board games if it does not work.

Playing with my daughter's boyfriend, I realized this death. I asked him about that, but his son was a die, and he has no idea what it is for. Any ideas?

D6 Faces 3, 4, 6
D6 Faces 7, 10, 11

I observe that 3 and 4 are the average of a d6, 6 and 7 are the average of a d12, and 10 and 11 are the average of a d20. But apart from that I have nothing. Google has failed me … or I've failed Google.

Who knows where this dice is?