Polygamy is a word that comes from late Greek. It can be translated as many marriages. It refers to any form of marriage where a person has more than one spouse. There is also a concept called group marriage. In group marriage, all the (adult) members of the group are responsible for all the children.
The form of mating where one male has sexual relations with many females is called polygyny. The form where there are many males for one female is called polyandry.
Historically, all forms have occurred in humans. Polygyny is the most common.
- Polygamy at socialsciencedictionary.org