What does the incident about queen atossa signify about the difference between the persians and the greeks?

The incident showed that while the Persian royalty got married to their female relatives in order to prevent succession challenges, it wasn't important to the Greeks because they had no royalty.

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It signifies the practice of sibling marriage or marriages within the royal family in order to keep the blood of royalty and succession within the family which is not the case with the Greeks.

Explanation:

Queen Atossa was the daughter of King Cyrus the Great of the Achaemenid. She got married to her own brother Cambyses II. Later on, she was also married to another Achaemenid king Darius with whom she bore the famous king of Persia Xerxes.

While it is customary for Persian royal families to marry within themselves as that the royal bloodline won't be tarnished or diluted, and the issue of succession won't be changed, Greeks have no such custom. They were able to intermarry with anyone.