Thurston’s paper Shapes of polyhedra and triangulations of the sphere is really remarkable. I’m writing about it in my next column for the Notices of the American Mathematical Society. Here’s a draft — which is also a much more detailed version of an earlier blog post here.
This is a companion discussion topic for the original entry at https://johncarlosbaez.wordpress.com/2024/10/30/triangulations-of-the-sphere-part-2/