Polygyny is the practice of being married to multiple women at the same time. It falls under the umbrella term “polygamy,” but in this case is specific to being wedding to multiple wives at the same time.
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In countries where polygamy is legal, generally it is only polygyny that is permitted. According to Murdock’s Ethnographic Atlas, more than half of recorded societies are polygynous. While polygamy is illegal in the United States the FLDS (Fundamentalist Mormon) tradition supports polygyny.