MathLapse Festival 2016 Winner. Parallel planes, which touch a surface of constant width from opposite sides, have always the same distance - a generalized diameter. The movie starts with curves of constant width, rotates them between parallel lines and deforms them, keeping constant width.
For surfaces this is repeated in anaglyph stereo: A sphere is deformed into a surface of constant width with rotational symmetry. This surface tumbles in a cube, touching all faces. Three more deformations to less symmetric surfaces and their tumbling follow.