National Science Foundation Vizzies Submission
I do most of my visual work in Mathematica (this is due to my lack of experience in computer graphics, suggestions or tips are welcome!). For people interested in playing around with some of this stuff themselves, below are some mathematica files together with short explanations of the mathematics and implementation.
Hopf & Seifert Fibrations
Regular Polytopes in 4D
Hyperbolic Reflection Groups
Projective Triangle Groups
The Allosphere is a 30ft diameter spherical