Polytwisters are a class of strange curved four-dimensional shapes related to uniform polyhedra and Hopf fibration. They were discovered by Jonathan Bowers circa 2007, who found 222 of these shapes plus three infinite families, and produced POV-Ray renders of their 3D cross sections.
I have a project to clean up and port the original POV-Ray code (unpublished) to a modern toolchain using Blender’s Python scripting capabilities. Computing the polytwisters as meshes enables professional-quality animations, as well as digital fabrication for realizing physical cross sections.
The project is ongoing and this is a placeholder landing page for it, sort of a teaser. All the code for producing these meshes is in a GitHub repo.