One of the more amusing details is that apparently there was a kind of cloak called mantion that was worn, not by civilians, but as Roman military dress. Sumner observes, as part of a discussion about short military cloaks:
Even though the physical differences between the sagum and the chlamys were always negligible, the word sagion (Latin sagum) was consistently used to describe the rectangular campaign cloak. If it was worn by a Magister Militum it was a purple colour (sagion alethinon), while the smaller version for use by the cavalry was still called the sagulum. Another short military cloak that we hear about was called the mantion (Chronicum Alexandrianum p. 102). This cloak was thrown back over both shoulders and fastened at the centre over the breast by a round brooch.
(emphasis mine). Sumner says nothing further about the military mantion, but since, like the later version worn by civilians, it fastened in the center of the chest with a round brooch, it may well have also been semicircular in shape. (Probably it was not rectangular, since the rectangular military cloak was called a sagum, but it could have been circular, or shaped like three-quarters of a circle).
Anyway, I know that costuming terms change meanings over time, but I found it interesting that the term mantion was already known to the earlier Romans, and applied to a garment with at least some similar attributes.