orientability

right|thumb|A torus is an orientable surface alt=Animation of a flat disk walking on the surface of a Möbius strip, flipping with each revolution.|thumb|The Möbius strip is a non-orientable surface. Note how the disk flips with every loop. right|thumb|The Roman surface is non-orientable.

In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "anticlockwise". It generalizes the concept of curve orientation, which for a plane simple closed curve is defined based on whether the curve interior is to the left or to the right of the curve. A space is orientable if such a consistent definition exists. In this case, there are two possible definitions, and a choice between them is an orientation of the space. Real vector spaces, Euclidean spaces, and spheres are orientable. A space is non-orientable if "clockwise" is changed into "counterclockwise" after running through some loops in it, and coming back to the starting point. This means that a geometric shape, such as 20px, that moves continuously along such a loop is changed into its own mirror image 20px. A Möbius strip is an example of a non-orientable space.