Transformation of a Boys Surface into a Steiners Surface and torus eversion

Abstract

The part 1 of the video shows a Boy s surface and a Steiner s Roman surface which are difficult to visualize without computer 3d graphics and demonstrates a continuous topological transformation between them. The part 2 of the video shows step by step how a two-dimensional torus with a hole can be turned inside out in R3 by a continuous topological operation without self-intersections. The torus without a disk, Boy s surface and Steiner s Roman surface are constructed as photorealistic two-sided and front-back coloured 3d objects.