You know, until you asked, I always thought that triplet, quads, quins etc were all always Identical twins.
I looked it up in my biology text book, but it didn't have anything to say on the topic (that I could find anyway) So well..yeah... I have nothing of any use to say I guess.
Say the natural incidence of identical twins is I (~1/100). Wouldn't the incidence of identical triplets be 2I2 (~1/5000)?
Since the probability of the initial zygote separating into identical twins is I, the probability of either resultant zygote further separating once should also be I, and when both resultants are considered together for triplets, 2I. Overall, then, the incidence of triplets should be 2I2.
I have identical triplet girls, so yes, it is possible, and is not known to be hereditary (the occurrence of identicals are equal across all ethnicities, backgrounds, etc). My girls are true identicals, not mirror image. Also, they are monochorionic triamniotic triplets (one big sac around three separate ones). As you've probably discovered, there is very little information as far as statistics regarding the phenomenon. From what the doctors figured, using the rate of identical triplets over all triplets (less than 4% of the time) and the rate of triplet births for every birth (?), it's about 1 in 4 million births. Hope this helps...
Oh yeah, monozygotic multiples have not increased more than the birth rate since fertility methods have increased because the two are not linked in a cause-and-effect relationship. Fertility methods often increase the number of eggs released before fertilization, not the ability of a zygote to fracture. Identicals are formed by the "freakish" splitting of the zygote on its own whim :) ~ Loren