orientable surface

A surface is orientable if a consistent concept of clockwise (or anticlockwise) rotation can be defined on the surface in a continuous manner. An orientable surface contains no subset that is homeomorphic to the Möbius band. Examples of orientable surfaces include the sphere, the torus, and the tori of higher genus.


Every orientable surface has an even Euler characteristic and can be embedded in three-space. When mapped into a Euclidean space, an orientable surface has two distinct sides. Compare with non-orientable surface.