Sphere eversion
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In differential topology, sphere eversion is a theoretical process of turning a sphere inside out in a three-dimensional space. It is possible to smoothly and continuously turn a sphere inside out in
Paper sphere eversion and Morin surface
Paper Morin surface (sphere eversion halfway) with hexagonal symmetry
halfway top
halfway side
Boy's surface
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In geometry, Boy's surface is an immersion of the real projective plane in three-dimensional space. It was discovered in 1901 by the German mathematician Werner Boy, who had been tasked by his doctora
Sphere eversion
…mathematical visualization: Half-way models: these consist of very special homotopies. This is the original method, first done by Shapiro and Phillips via Boy's surface, later refined by many others. The original half-way model homotopies were constructed by hand, and worked topologically but weren't minimal. The movie…
Model of a Boy's surface in Oberwolfach Research Institute for Mathematics