or . 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.

Examples

Most surfaces encountered in the physical world are orientable. Spheres, planes,

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