Boy's surface

In geometry, Boy's surface is an immersion of the real projective plane in 3-dimensional space found by Werner Boy in 1901. He discovered it on assignment from David Hilbert to prove that the projective plane could not be immersed in 3-space.

An animation of Boy's surface

Boy's surface was first parametrized explicitly by Bernard Morin in 1978.[1] Another parametrization was discovered by Rob Kusner and Robert Bryant.[2] Boy's surface is one of the two possible immersions of the real projective plane which have only a single triple point.[3]

Unlike the Roman surface and the cross-cap, it has no other singularities than self-intersections (that is, it has no pinch-points).


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