High Quality Content by WIKIPEDIA articles! In mathematics, the real projective plane is a non-orientable two-dimensional manifold, that is, a surface, that has basic applications to geometry, but which cannot be embedded in our usual three-dimensional space without intersecting itself. It has Euler characteristic 1, hence a demigenus (non-orientable genus, Euler genus) of 1. A common construction of the real projective plane is as the space of lines in R3 passing through the origin.

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