In a typical polygamist society, including the FLDS, men have multiple wives. The women have only one husband. Sometimes wives are reassigned to other men, but each woman has only one husband at a time.

Technically, a polygamist marriage is any marriage where a person has more than one spouse. Most polygamist marriages have one man and multiple women, also called polygyny. This is the most common form of polygamy, (and also the one found lately in the news in the compound in Texas.) There do exist forms of polygamy (or group marriage) which involve multiple members of both sexes, but they are pretty rare. So to answer your question specifically... no, it usually doesn't mean the wife (wives) have more than one man available.

(Answer is from a non-Polygamist)A little background 1st... According to the FLDS, Polygamists, a man must have more than 3 wives to go to Heaven. A polygamist wife needs a good Polygamist Man to get in...she rides his coattails, basically. So we have the priciple equasion of 1 man + many wives. In the current FLDs, under convicted sexual offender, Warren Steeds Jeffs law, he can if he sees fit--dismantle families and re-assign wives and children from one man to another man within the FLDS community. So indeed, one wife could have more than one husband but never more than one at a time. (While a man enjoys as many wives as he likes) The original FLDS law of wife and child re-assignment was to protect women and children from abuse, or to replace a wife after a death.

It appears to me, from all I've read, that sects which practice polygamy allow men to have multiple wives ..... but the wives are stuck with just the one man.

Most modern polygamy involves a man with multiple wives(polygyny). A wife with multiple husbands (polyandry) was never as common but it has occured in history. Group marriage (both having multiple spouses) is even more rare.

I assume you refer to the fact that Joseph Smith was sealed to the wives of other men. In Mormon polygamy, a man may have multiple wives, but a woman can only have a single husband. Joseph Smith was never married to a woman who was legally married to another man at the time. Joseph did not have sex with any such women; those women stayed with their husbands.

He was prolific. No doubt about that.

"The term polygamy (a Greek word meaning "the practice of multiple marriage") is used in related ways in social anthropology, sociobiology, and sociology. Polygamy can be defined as any "form of marriage in which a person [has] more than one spouse." In social anthropology, polygamy is the practice of marriage to more than one spouse simultaneously. Historically, polygamy has been practiced as polygyny (one man having more than one wife), or as polyandry (one woman having more than one husband), or, less commonly as group marriage (husbands having many wives and those wives having many husbands). (See "Forms of Polygamy" below.) In contrast, monogamy is the practice of each person having only one spouse. Like monogamy, the term is often used in a de facto sense, applying regardless of whether the relationships are recognized by the state (see marriage for a discussion on the extent to which states can and do recognize potentially and actually polygamous forms as valid). In sociobiology, polygamy is used in a broad sense to mean any form of multiple mating. In a narrower sense, used by zoologists, polygamy includes a pair bond, perhaps temporary." Source and further information: http://en.wikipedia.org/wiki/Polygamy

Polygamy is a general term, polyandry and polygyny refer to multiple husbands for one woman or multiple wives for one husband. What you describe is group marriage. Polygamy as practiced by the FLDS, or by Mormons a century and a half ago was polygyny or one husband with multiple wives. Under that model, the wife has only one ("authorized") partner.