A surface is orientable if it does not contain any Möbius bands.

The orientable surfaces are the sphere, the torus, and the tori of higher genus. In more generality, these are called the sphere with n handles (where n may be zero).

The orientable surfaces all have even Euler Characteristic.

Every orientable surface can be embedded in three-space. An orientable surface mapped into a Euclidean space will have two distinct sides.

See also:

[More] Non-orientable surfaces

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8/12/94 dpvc@geom.umn.edu -- The Geometry Center