Half-identical twins are also called polar body twins. At the end of the normal process of ovulation, the developing egg divides into two cells. Each cell has the same number of chromosomes in the nucleus, but different amounts of cytoplasm. The bigger cell (with most of the cytoplasm) is the egg, and the much smaller cell with very little cytoplasm is called the polar body. The polar body usually degenerates and dies.
Polar body twins are theoretically caused when the polar body is fertilized by one sperm at the same time the egg is fertilized by a different sperm. In theory, this results in twins who share half their genes in common (from the mother), but the other half of their genes are different because they come from two different sperm cells.
In theory, polar body twins would share 75% of their genes in common, so polar body twins are also called half- identical (since identical twins share 100% of their genes in common, and fraternal twins share an average of 50% of their genes in common).
However, there is no proof that polar body twinning has ever occurred. And there are some theoretical arguments that it doesn’t happen. For example, genetic recombination occurs during the formation of eggs, so the maternal DNA in the egg may not be identical to that in the polar body. Also, with very little cytoplasm, it is unlikely that a fertilized polar body would be able to survive and develop into a normal embryo and fetus. There are no definitive tests to confirm polar body twinning, so it remains a theory only.