I'm currently reading "The Cartoon History of the universe" by Larry Gonick. When talking about Sumer, the author says that "around 2400 B.C., the reformer Urukagina banned the practice [women marrying more than one husband] in no uncertain terms: "If a woman takes a second husband, her teeth should be bashed with bricks" ". Is this historically accurate? If so, what was the incentive to ban this type of behaviour?
In addition to such changes, two of his other surviving decrees, first published and translated by Samuel Kramer in 1964, have attracted controversy in recent decades. First, he seems to have abolished the former custom of polyandry in his country, on pain of the woman taking multiple husbands being stoned with rocks upon which her crime is written. Second is a statute stating that "if a woman says [text illegible...] to a man, her mouth is crushed with burnt bricks."
Wikipedia undermines Gonick's assetion; it appears that Gonick may have conflated two distinct edicts.
If you're asking whether the penalty was ever applied, I have no information.
If you're asking Why Urukagina would impose this penalty, there are some theories. Marlyn French asserts that this is the beginning of a trend of degradation of women, but I think it is premature to ascribe that as the sole or even primary motivation. Other information in the wikipedia article implies that he expanded the role and property of women in the royal household, which seems to be in tension with a primary motivation of degrading women.
@Tom Au has offered speculation as to Urukagina's motivation, which seems plausible, however the wikipedia article on polyandry suggests that some cultures do recognize partible paternity, which would address the issues that Mr. Au raises. Partible paterntity seems to be most prevalent in the Amazon and in Hawaii - I didn't see any reference to the concept in Urukagina's time/context. I simply don't have sufficient evidence to confirm or deny the assertion that Urukagina's edict was designed to ensure clear lines of heredity.
A woman can have a child by her husband even if he is "seeing" other women. Society will always know which woman the child came from (and will make inferences about the man).
On the other hand, only one man can produce a child with a woman at any given time. If a woman is "married" to two men simultaneously, the paternity of the child will be "clouded" (at least in the days before DNA testing). The issue of the child's succession/inheritance will be cloudy, and this would be a major reason for society to discourage a relationship between a woman, and two or more men.
Because of that fact, the Sumerians practiced only "fraternal" polyandry, that is that a woman could marry only two brothers, who were presumably from the same family. But Urakagina thought even that was going too far. http://www.spiritus-temporis.com/polyandry/ He was a "reformer" who inveighe against "corrupt" practices, mainly in the fiscal realm, but also in civil law. http://civislibertas.com/urukaginas-code/
The penalty for polyandry was death by thrown stones, "upon which her crime was written." The "bashing of teeth with bricks" was for a speech crime.