Has there ever been double twins born?

You can have twins from two eggs being fertilised or two sperms simultaneously fertilising an egg. Have these two things ever both happened so that there are identical twins and also an unidentical twin?
Update: OK, it's been explained to me that the egg splits in two then gets fertilised or there are two different eggs. Premise of the question still exists - has there ever been identical twins born with unidentical?
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