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
Model of a Boy's surface in Oberwolfach Research Institute for Mathematics
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
Boy's surface
…axis will leave the surface looking exactly the same. The Boy's surface can be cut into three mutually congruent pieces. Boy's surface can be used in sphere eversion as a half-way model. A half-way model is an immersion of the sphere with the property that a rotation interchanges inside and outside, and so can be…
Paper sphere eversion and Morin surface
Paper Morin surface (sphere eversion halfway) with hexagonal symmetry
halfway top
halfway side