Ever heard of twins who celebrate their birthdays months apart? What about twins who have different biological fathers? This seems impossible, but it turns out that both of these things happen. These incidents are rare, but real.

As we mentioned earlier, some women can release more than one egg during ovulation. In some exceptional instances, these eggs are released at different times. Perhaps at 12 or even 20 days apart. Now, let's say both of these eggs are fertilized shortly after they are released. The woman conceives twins, but on two separate dates. Since the dates of conception differ, so will the dates of delivery. The twins could be born a couple of weeks or a month apart. This is known as superfetation.

When a mother releases more than one egg during ovulation and has intercourse with more than one male during that time, it may result in superfecundation twinning. Two distinct sperm from two separate individuals fertilize the two eggs the woman ovulates. Obviously, the twins resulting from superfecundation are dizygotic.

Some research suggests another type of twin called "polar body" or "half-identical" twins. This type of twin is supposed to occur when one egg splits before fertilization and is then fertilized by two separate sperm. It is believed that these twins share 75 percent of their
DNA; they share identical DNA from the egg and different DNA from the sperm.

Original text:
http://science.howstuffworks.com/twin5.htm

MIRROR-IMAGE TWINS
Mirror-image twins occur only in identical twins. Here is how it happens: in approximately 23 percent of identical twins the egg splits later than usual, most often day seven or beyond. The original right half of the egg becomes one individual and the original left half becomes the other. These twins will often have "mirror images" of their features, such as hair whorls that run clockwise in one and counter clockwise in the other, a birthmark on the right shoulder of one and the left shoulder of the other, etc. There is no specific test for determining if twins are mirror-image. The determination is made by observation only, and the twins must be monozygotic, or identical.

This may be a partial explanation for the fact that a little over one third of identical twins are left-handed, double the rate in the general population. In extreme cases all of the internal organs are reversed in one of the twins, with the heart on the right, the liver on the left and the appendix on the left.

POLAR BODY TWINS (HALF-IDENTICAL)
Polar body twinning is very unusual and very rare. The process is quite complicated. The polar body appears when the egg has been developing, even before fertilization. It is a small cell that does not function and will usually degenerate and die. It is thought that in some cases, when the egg is old, the splitting off of the polar body takes place in an abnormal way. It then becomes larger, receives more nourishment, and does not die as it usually does. Instead, it acts as a second egg. The polar body and the egg share identical genes from the mother, but they may then be fertilized by two separate sperm from the father. This will result in twins who share half their genes in common (from the mother) and the other half different (from the two sperm). They share some features of identical twins and some features of fraternal twins and thus are so-called half-identical twins.

MIXED CHROMOSOMES OR CHIMERISM
Another form of twinning that has been identified is called chimerism. This is thought to occur if two separate sperm fertilize two separate eggs which then fuse, producing individuals with different sets of chromosomes. Some have been identified that have more than one distinct red blood cell type and individuals who are both XX and XY (the sex chromosomes - XX being female and XY being male.) This phenomenon might also be associated with fused placentas causing intermixing of the circulations. It is very rare, and fewer than twenty-five cases have been identified. It is more common in other mammals, such as calves.

Original text:
http://www.nomotc.org/library/twinning_facts.html