Cospace

Every region in a roundspace has an opposite and is not peripheral. Producing a roundspace from a space is easy, and results in boundaries through a center point. The boundaries through the center point map to points on a section plane in the cospace. Sections of the roundspace are great circles formed by planes through the center point. Vertices in the roundspace have diameters through the center which map to subvertices in the cospace section. The cospace section has boundaries mapped to vertices in the roundspace. By adding an equator plane to the roundspace, the cospace section has one region per roundspace section. The cospace section has peripheral regions. Thus depending on roundspace rotation, there are special sections in the space, corresponding to peripheral regions in the cospace section.