Some tools and colleagues. I got bored updating this in about 2008.
3D CAD software. Not the shiniest, but it has capability in both NURBs and mesh modeling, as well as strong scripting and support for many file formats, all of which make it work well with other software. No one tool does everything, so my wheelhouse is the tool that plays well with others.
A plug-in for Rhino that's useful for making organic and curved forms. In 2011 it was bought by AutoDesk, and I don't know what its future holds.
A photorealistic renderer that purports to simulate the physical nature of light. It has settings like an SLR camera and specifies materials by their optical properties. It's extremely slow, but I use it because it's the only renderer that makes any sense to me.
Freeware for studying minimal surfaces, relaxing knots, and many other things that are over my mathematical head. This is my secret weapon for mesh conditioning.
Qhull Freeware for computing convex hulls and Voronoi networks. Again, much of what this does goes way over my head; but I can report that the parts I can understand work well.
Ineffably gorgeous strange attractors.
A tool for generating and visualizing Seifert Surfaces.
A topology-based mesh modeler.
The net is littered with tools like these, single-purpose utilities written by and for fans of particular concepts. I love them, but I can't begin to mention even all the ones that I've used. They vary greatly in documentation and ease-of-use. They're like unexpected windows in the cathedral of mathematics.
This comprehensive tool needs no introduction, but let me remind you that it can write STL files, which is the standard format for 3D printing. More could be done with this.
A user-friendly 3D printing service bureau, which also allows you to sell printed designs. Good pricing on a nice selection of materials including steel, ceramic and precious metals. If you're new to the field it's a great place to check out a variety of materials. If you're not new you may find competitive prices and good selection here. I don't often need 3DP parts other than metal, but when I do I get them here.
Steel printers and printing services. I make most of my sculpture with this process, and the accuracy, freedom and strength of these parts is excellent. This company is mainly industrial/wholesale, so they're not be the easiest place to get started, but once you have gained some metal printing experience at Shapeways or elsewhere, if you need a lot of steel parts and a direct relationship with a supplier, these are the guys.
Laser Crystal Awards
High-end subsurface laser etching. 2D photos or 3D designs, quantities one to thousands, they can do it.
The best quality subsurface laser etching that I know of.
Reinmuth Bronze Studio
A full-service bronze foundry in located Oregon, with special expertise in geometrical sculpture. Steve Reinmuth is himself an extraordinary sculptor, and also a fantastic caster and finisher.
There's an enormous flowering of math/art going on. My colleagues in this field are now legion, so I'll just mention a few old friends and favorites. Lee Krasnow and Oskar van Deventer's mechanical puzzles. George Hart, and his daughter Youtube sensation Vi Hart. Vladimir Bulatov, who has knocked off probably more of my stuff than anyone else. Paul Nylander and Torolf Sauermann's fantastic renderings. Brent Collins and Bjarne Jespersen's credibility-stretching wood carvings. Erwin Hauer and Robert Engman, great geometrical sculptors of the 20th century, and my fathers in art. If you ought to be on this list and aren't, I can only say that it's not personal, there are just an awful lot of you.
Two organizations that run annual math/art conferences, and have many artist and resource links:
International Society for the Arts, Mathematics, and Architecture (ISAMA)