Torus eversion with two klein bottles. Invented by Derek Hacon around mid 1970s(?)
References:
Derek Hacon's notes: http://www.math.utah.edu/~hacon/sphereeversion.pdf
Circle Deformation in Hacon’s Sphere Eversion by Yongheng Zhang: https://archive.bridgesmathart.org/2021/bridges2021-265.pdf
Mathologer's video: https://www.youtube.com/watch?v=ixduANVe0gg
Animation by Arnaud Chéritat: https://www.youtube.com/watch?v=kQcy5DvpvlM