Wiki:
Forms of polygamy
Polygamy exists in three specific forms, including polygyny (one man having multiple wives), polyandry (one woman having multiple husbands), or group marriage (some combination of polygyny and polyandry). Historically, all three practices have been found, but polygyny is by far the most common.
Polygyny
Polygyny is described as when a man is either married to or involved in sexual relationship with a number of different females at one time. This is the most common form of polygamy. [citation needed]
Polyandry
Polyandry is a mating practice where a woman has more than one male sexual partner simultaneously. Polyandry was traditionally practiced among nomadic Tibetans including Nepal and parts of China, where it meant that two or more brothers share the same wife.
Group marriage
Group marriage, or circle marriage, may exist in a number of forms, such as where more than one man and more than one woman form a single family unit, and all members of the marriage share parental responsibility for any children arising from the marriage. Another possible arrangement not thought to exist in reality, although occurring in science fiction (notably in Robert Heinlein's The Moon Is a Harsh Mistress), is the long-lived line marriage, in which deceased or departing spouses in the group are continually replaced by others, so that family property never becomes dispersed through inheritance.
Strictly speaking, cohabitation involving three or more sexually-involved people does not count as polygamy unless the participants at least claim to be married..
Bigamy
Bigamy is when one individual is married to two people at the same time; a person doubly married is a bigamist. Many countries have specific statutes outlawing bigamy, making any secondary marriage a crime.
Note that these laws aren't limited to cases of traditional polygamy, where the spouses know about each other. They also cover cases such as a man who breaks up with his wife, and without divorcing her, marries another woman. It even covers the occasional case of a man who sets up a second family with a second wife, keeping his dual marriage a secret from one or both of them. In both of these cases, the effect of these laws is to protect people from being married under false pretenses.
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Bigamy still works as used in the story as it refers to a person instead of sex. Its also our local legal term for the crime of multi-marriage... so ... again... it still works as used.
