Mirror image twins are identical and have mirror image differences but are genetically identical which means they have the same DNA.
A set of mirror-image twins will have similarities like a mole. One twin would have it on his left arm while the other would have it on his right. Another common feature is one twin being left handed, while the other is right handed. For male twins, the swirl of hair crown is often in the opposite direction.
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Mirror Twins are always monozygote twins. This does not mean that fraternal twins won't be a righty and a lefty - if your family tends to run left handed.
Ferternal twins don't look alike, but twins do
The fact that twins run in families is actually a myth. The odds of twins having twins is the same as a non-twin having twins. That is about 1 in 33.
Most people will answer this by explaining that the twins will run the same risk are normal adults. However, if the twins are monozygotic they may also be "mirror-twins", in which one twin would have an increased chance of displaying situs inversus, a condition where the organs are flipped (mirrored to other twin). This in and of itself isn't harmful, but the origins of situs inversus are believed to be in the earliest stages of development, arising from cilia that move clockwise instead of counter-clockwise, thus moving the cells that will form organs to the wrong side. Going back to questions of infertility, it is known that this wrong-turning cilia cannot play a normal roll in some biologic functions, including driving the bending movement required for sperm (cilia structures of the tail) to be motile. In this way, male infertility (sterility) could theoretically be affecting at a higher incidence in man mirror twins with situs inversus.
Fraternal twins are more popular.