You mean polyamory.

Polygamy is 1 man to multiple women. Polyamory is between more then two people of any gender or combination of genders.

Grand parent comment is talking about one man many women marriages as having higher rates of abuse, so your quibble here seems out of place.

But you're also wrong! Polygamy refers to any marriage that has more than two partners, gender identity is irrelevant.

One man many women is polygynyz one woman many men is polyandry. Polyamory is multiple partners.