Orientable

Orientable surfaces

For an orientable surface, a consistent choice of "clockwise" (as opposed to counter-clockwise) is called an orientation, and the surface is called oriented. For surfaces embedded in Euclidean space, an orientation is specified by the choice of a continuously varying surface normal${\displaystyle \mathbf {n} }$ at every point. If such a normal exists at all, then there are always two ways to select it: ${\displaystyle \mathbf {n} }$ or ${\displaystyle -\mathbf {n} }$. More generally, an orientable surface admits exactly two orientations, and the distinction between an oriented surface and an orientable surface is subtle and frequently blurred. An orientable surface is an abstract surface that admits an orientation, while an oriented surface is a surface that is abstractly orientable, and has the additional datum of a choice of one of the two possible orientations.