Monozygotic (identical) twins come from a single fertilized egg that splits. But what if the egg splits and then each half meets a sperm? That's the proposed theory for polar body or "half-identical" twins, twins who are very much alike but aren't a 100 percent DNA match.
Two girl twins can be either identical or fraternal (monozygotic or dizygotic). Two boy twins can be either identical or fraternal (monozygotic or dizygotic). A set of boy/girl twins can only be fraternal (dizygotic). Boy/girl twins cannot be identical (monozygotic).
Mirror twins—or mirror image twins—aren’t really a category of twins, like identical/monozygotic twins. Rather, the term “mirror twins” describes a characteristic of some twins, where their features appear asymmetrically -- that is, on opposite sides.
But parasitic twins are not to be confused with conjoined twins. Parasitic twins are characterized by one fully healthy individual with its parasite who is fully dependent on the health twin for substance and survival. Moreover, the parasitic twin can be joined at any part of the healthy twin.
Monozygotic twins cannot have different fathers. However, fraternal twins are the result of hyperovulation, the release of multiple eggs in a single cycle. Superfecundation describes a situation where the eggs are fertilized by sperm from separate incidences of sexual intercourse. In a case where a woman has sex with different partners, the twins could have different fathers.