Editing Orientability (section)

===Examples===
Most surfaces encountered in the physical world are orientable.  [[Sphere]]s, [[plane (mathematics)|planes]], and [[torus|tori]] are orientable, for example.  But [[Möbius strip]]s, [[real projective plane]]s, and [[Klein bottle]]s are non-orientable. They, as visualized in 3-dimensions, all have just one side.  The real projective plane and Klein bottle cannot be embedded in '''R'''<sup>3</sup>, only [[immersion (mathematics)|immersed]] with nice intersections.

Note that locally an embedded surface always has two sides, so a near-sighted ant crawling on a one-sided surface would think there is an "other side".  The essence of one-sidedness is that the ant can crawl from one side of the surface to the "other" without going through the surface or flipping over an edge, but simply by crawling far enough.

In general, the property of being orientable is not equivalent to being two-sided; however, this holds when the ambient space (such as '''R'''<sup>3</sup>  above) is orientable. For example, a torus embedded in 
:<math>K^2 \times S^1</math>

can be one-sided, and a Klein bottle in the same space can be two-sided; here <math>K^2</math> refers to the Klein bottle.