No, this feels more like sorcery and cheating than the other ones... I could have sworn there was some cutting and pasting done behind the scenes when the parts overlapped each other Hacon's Half-Torus and Thurston's Corrugations were very simple and elegant in comparison to this... witchcraft
Fun fact, according to all laws of topology, turning a sphere outside in is really easy, since you pull the inside out Because the material in topology can pass through itself.
Bro, it's so easy. It might look like they are crossing, but they are not. I am simulating it in the 4th dimension and it works. Come on bro, why don't you get it?