Uh, you've all gotten the definition of polygamy not quite right.

Polygamy is when either a man or a woman has multiple spouses.

PolyGYNY is when only the man may have multiple spouses

PolyANDRY is when only the woman may have multiple spouses.

PolyGAMY is an umbrella term that covers both polygyny and polyandry.

Polygamy is not synonymous with polygyny, even though it is the most common type.