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:**

- Non-orientable surfaces

* 8/12/94 dpvc@geom.umn.edu -- *

*The Geometry Center*