Orientability
In the Euclidean space, R3 is called orientable if a two-dimensional figure (for example, 
) cannot be moved around the surface and back to where it started so that it looks like its own mirror image (
). Otherwise the surface is non-orientable. A concept connected to this is chirality. This means that no matter what, a human right hand, cannot be rotated in such a way that it becomes a human left hand. The right hand is therefore orientable.
Orientability Media
A torus is an orientable surface
The Möbius strip is a non-orientable surface. Note that the fiddler crab moving around it has left and right flipped with every complete circulation. This would not happen if the crab were on the torus.
The Roman surface is non-orientable
Animation of the orientable double cover of the Möbius strip.
