A new kinds of twins, called "semi-identical" twins were just recently identified by scientists. These types of twins share their maternal DNA, but only half of their fathers DNA. This is very rare, because in this state two sperms penetrate one egg. This happens in about 1% of the population, however, most of the time, these 'triploids' do not live. Well, in this case, they did. Scientists suspect that in order for this to happen, one of the two conditions have to be met. First the egg divided before the sperm penetrated, this allowed two identical eggs, and two different sperms to fertilize them. Second, and the more likely possibility is that two sperm fertilized one egg simultaneously, and created a triploid. Then, during the second stage the triploid underwent changes to account for the extra set of chromosomes present. This process is still unclear to scientists. One of the two twins has been identified as an "intersex" twin with 5% XY, and 95% XX, and the other identified as male, has 50% XX and 50% XY.
http://www.time.com/time/health/article/0,8599,1603799,00.html
I found this article interesting because sometimes we think that we have figured out what there is to know about some of the most well known processes, but then a case like this pops-up and proves us wrong. Overall, it was worth reading.