Polygamy is a marriage which includes more than two partners. When a man is married to more than one wife at a time, the relationship is called polygyny

Polygyny

Polygyny is a form of marriage in which a man has two or more wives at the same time. In countries where the practice is illegal, the man is referred to as a bigamist or a polygamist...

, and there is no marriage bond between the wives; and when a woman is married to more than one husband at a time, it is called polyandry

Polyandry

Polyandry refers to a form of marriage in which a woman has two or more husbands at the same time. The form of polyandry in which a woman is married to two or more brothers is known as "fraternal polyandry", and it is believed by many anthropologists to be the most frequently encountered...

, and there is no marriage bond between the husbands. If a marriage includes multiple husbands and wives, it can be called group marriage

Group marriage

Group marriage, also known as multi-lateral marriage, is a form of polyamory in which more than two persons form a family unit, with all the members of the group marriage being considered to be married to all the other members of the group marriage, and all members of the marriage share parental...

.