Original: Orientable surfaces A surface S in the Euclidean space R3 is 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.
Simplified: 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.