This 2001 article from the Colonial Williamsburg Journal offers a fairly eloquent exposition of certain aspects of hexagonal symbolism that are worth noting. I found the hexagons themselves fairly interesting too—particularly in contrast with the rather hexagon-poor architecture of colonial New England that I'm more familiar with. I've never been a great fan of Anglicanism, or High Church aesthetics in general, but the Puritans clearly couldn't design an interesting building if their lives depended on it—indeed, they probably would've interpreted a hexagonal cupola as a sign of idol worship or something.
Here we see, apparently, a cuneiform hymn to Iddin-Dagan, lugal of Larsa, from the 19th century BC, inscribed on a hexagonal artifact of some sort. It is my understanding that the Sumerians of yore made similar inscriptions on otherly-shaped blocks as well—square, pentagonal, etc.—but I would like to think there was some religious significance to the choice of a hexagon here.