I know the question seems to make no sense, but I swear I've seen them. Twin siblings who look perfectly identical in every way except for their sex. If you've ever seen that show John and Kate Plus 8, you'll know what I mean. They have six-tuplets, 3 girls and 3 boys, and the girls look identical to each other and so do the boys.

 

Can this ever happen?

No. However, if you bear in mind that regular siblings often look very similar to one another, and the fact that fraternal twins are exactly the same age on top of that, it shouldn't be all that surprising that some look spookily similar without being identical, even if they are different sexes.

I am sure if you take a closer look, you will see that they are not identical.

It's also theoretically possible for two separate eggs to be fertilized (fraternal twins), and each of those eggs to divide (identical twins), thus producing the effect seen on the show.

 

However, I suspect it's more a case of cleverly casting two sets of identical triplets who just happen to be very similar in appearance (much like finding a body double, but 3 of them in one).

It's also theoretically possible for two separate eggs to be fertilized (fraternal twins), and each of those eggs to divide (identical twins), thus producing the effect seen on the show.

 

However, I suspect it's more a case of cleverly casting two sets of identical triplets who just happen to be very similar in appearance (much like finding a body double, but 3 of them in one).

 

I hardly watch the show, but I'm pretty sure they are all siblings in real life.

http://en.wikipedia.org/wiki/John_and_Kate_Plus_8

 

Apparently so.

What are the odds of two different sperm having the same 22 chromosomes, but one with an X and the other with a Y, and two different eggs having the same 23 chromosomes?

Almost nil, because there's also 'crossing over', which will further mix the genetic material.