My question actually applies to identical multiple births of any number, but was stimulated by the recent news of a mother being pregnant with identical quadruplets, and how unlikely that is.
Give that the babies have not been born yet, how is it determined that they are identical quadruplets rather than fraternal quadruplets? Even the fact that they are all the same gender would not necessarily imply that they are identical. 
They either have cell samples from all 4, or they have some other evidence that the fetus started as a single cell and later split. Dunno what that evidence might be.
Monozygotic (identical) multiple births frequently share the same placenta and might even have a single amniotic sac. Fraternal multiples always have separate placentas and amniotic sacs.
So, if on ultrasound you have four babies all sharing a single placenta you have identical quads.
That’s what comes to mind first, there may be other ways to know I’m not familar with.
OK - Thanks!