Oh, just saw your latest post. What annoys me is that they keep calling them "spiritual marriages." To me, that term implies that the marriage is purely Platonic, without any sexual contact. Extralegal or alegal would seem more appropriate terms.
mek, where are you getting your definitions? Going by the dictionary definitions I've seen, by common usage, and by simply looking at the roots of the words, you would appear to be quite mistaken. So far as I know:
Polygamy is any marriage with more than two participants. "Poly" refers to "many" and "gamy" refers (roughly) to marriage.
Polygyny means having more than one female sexual partner, regardless of marriage.
Polyandry means having more than one male sexual partner, regardless of marriage.
The only term I know of for a marriage with multiple male AND female partners is "complex marriage," as in the Oneida Colony.