Thanks. The http://en.wikipedia.org/wiki/Polygamy has phrases below:
<quote>
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).
--
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.
</quote>
Hmmm. The 'from a single family' part is somehow puzzling ...