No, the children of two female identical twins impregnated by the same man would not be considered twins. While the children would share the same biological father, they would not be genetically identical like their mothers. Here's why:
Genetic Material from Father: Each child would inherit 50% of their genetic material from their biological father. Since the father's genetic contribution is unique for each child, the children would not be genetically identical to each other.
Genetic Material from Mothers: The two female identical twins (mothers) would share the same genetic material because they are monozygotic twins. This means they have identical DNA, as they originate from the same fertilized egg that split into two embryos. However, when they each pass on their genetic material to their children, there would be random genetic recombination during the process of meiosis. As a result, the children would not receive identical DNA from their mothers.
Genetic Diversity: The combination of genetic material from both parents (father and mother) leads to genetic diversity in each child. Even though the mothers have identical DNA, the children would still have unique genetic profiles due to the random assortment of genetic material during conception.
Therefore, the children would be half-siblings, not twins, with 50% of their genetic material coming from the same father and approximately 50% coming from each of their respective mothers, who, in this case, are identical twins.