I guess England was never a monarchy, what with all those earls, dukes, and barons running around. Sounds like a polyarchy to me! I understand that the three main Gods of Hinduism (who presided over the three main phases of existence) were incarnations of the same God, but my understanding was also that there were other, minor Gods who were not. Regardless, I envision polytheism more like the Greek polytheism. Tons of gods, contending against one another, none with absolute dominance. Contrast that with Christianity, which has one God (with three aspects) that has absolute dominance over everything. And yes, you are right that the exact nature of Christ served as a point of division among Christians in the past (which, in itself, is silly), but all of them agreed that they were in Monotheistic religion. Christ, whatever is nature, served God the Father, no matter how they were related. Just because there's a prince and a king doesn't mean the country isn't a monarchy. There were also other dividing factors between the east and west church, such as whether or not "icons" were sinful and, most importantly, earthly power over one another.