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- adj. Not able to be oriented.
Sorry, no etymologies found.
The Pn, that is the real projective spaces, have a remarkable property: for even dimensions n they are nonorientable, but for odd dimensions orientable.
A space is orientable, if a tornado (or any other spinning top), when moving along any closed path, returns to its starting point with the same sense of gyration with which it started, and it is nonorientable if along some closed path the sense of gyration is reversed.