The didicosm is a three-dimensional space that belongs to the platycosm family, and has a flat geometry and a finite volume with no boundary. The didicosm is formed by taking a rectangular prism, identifying its faces, and creating a kaleidoscopic view, which shows different screw rotations. The loops in the didicosm are classified based on the number of times they wind around a space and can be represented by pairs of integers. The fundamental group of the didicosm is infinite and can be represented by a group presentation. While loops on a torus can indicate the presence of different “holes,” the idea of holes in spaces is mainly based on the existence of a loop that is not the boundary of any region.
https://www.gregegan.net/DIDICOSM/Loops/Loops.html