One-Sided Surface

a surface that, in contrast to, for example, the sphere or square, does not have two different sides. More precisely, let us suppose the surface has a normal continuously dependent on a point. By taking the normal vector at any point on the surface and continuously shifting it along a closed path, we can reach the initial point with a vector opposite in direction to the original vector. The simplest one-sided surface is the Möbius band. The class of one-sided surfaces in three-dimensional space coincides with the class of nonorientable surfaces.