This work comprises an effort to develop a framework to construct various space geometries in 3 and higher dimensions, and also in flat and curved settings. Such construction is based on scientific knowledge, existing approaches, and own approach and imagination. Higher dimensional geometries are presented in forms of 2 and 3 dimensional projections. Curvature settings are considered along regular object bending and also gravitational space warping, however the exact space curvature is rendered according to a proposed methodology that makes use of glissette geometric formation to resolve the shape of space under expansion and contraction conditions. The resulting geometric forms point to potential various physical shapes of the universe and possibly offer an opportunity to help expand our imagination and understanding of the universe.