As Rhea Cole mentioned previously, the shape is comparable to those emblems worn by some companies of fireman, as well as some fraternal organizations dating back to, and even prior to, the Civil War. This (cropped) image of three soldiers from the Fourth Michigan Infantry (probably taken in the fall of 1861), shows a private wearing in the center wearing a brass belt plate with an identically shaped cross in its center. I know it to be the same styled cross and a brass belt plate, because I've seen at least two examples of it for sale over the years. One of the companies from the 4th Michigan had recruits that had been firemen in Detroit at the time of their enlistment, so this soldier could have been one of them.
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