What If a 3D Surface Passes Through Itself?

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Can a surface have no edges, only one side, and pass through itself in 3D without creating a single sharp crease? In 1901, Werner Boy answered David Hilbert's challenge by proving that the real projective plane RP^2 can be smoothly immersed in 3D Euclidean space. Unlike the Klein bottle, Boy's surface features a single triple point where three sheets cross and a stunning 3-fold cyclic symmetry. Here, the Kusner-Apery rational parametrization is traced as an unbroken continuous helical manifold.

Related Video: Topology & The Impossible 3D Knots (https://youtu.be/0mvqG8cNyOw)

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