Polygamy
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Polygamy is a word that comes from late Greek. It can be translated as many marriages. It refers to any form of marriage, where there is more than one spouse.[1]
The form where one man has sexual relations with many women is called polygyny, the form where there are many men for one woman is called polyandry. There is also a concept called group marriage, which is a combination of ployandry and polygyny. In group marriage, all the (adult) members of the group are responsible for all the children.
Historically, all forms have occurred. Polygyny is the most common though.