What do you teach at Stony Brook?
I teach a range of courses including some on computer-aided sculpture and algorithms for 3D design. As far as I know, my Computers and Sculpture class is the only course in the universe specifically about the various ways in which computer technology is applied to sculpture.

Why the fascination for three dimensional space?
We are stuck in a 3D universe and we have evolved to perceive and enjoy its richness. Sculpture helps one appreciate both the possibilities and the limitations of space.

What is your Encyclopedia of polyhedra?
That is web resource I wrote to systematize a great deal of information about polyhedra, including so me mathematical gems and an appreciation for their history and beauty. It is illustrated with 3D models in VRML, which was the state of the art in the mid 1990s when I wrote it, but the technology is a bit dated now. I'd like to find a student to do a project converting everything a more modern format.

What 3D software tools do you use?
I use many different tools, but commercial software doesn't have features I need for the kinds of mathematical structures that interest me. So mostly I write my own 3D sculpture CAD tools, which I then use in design. This makes me want new features, so I am constantly varying and editing my software.

Would you recommend any of them?
The tools I write are just for me. Nothing is stable or documented for release. I'm mainly interested in producing actual sculptures, and the software tools are just one of many steps along the way.

What kind of person would you recommend the software tool Mathematica to?
To use it well, you need some mathematical maturity, an understanding of basic software concepts such as recursion, and means to get a copy inexpensively. I expect it is far too expensive for individual artists to consider purchasing.

You wrote a paper about procedural generation of sculptural forms, could you in laymans terms explain this to us?
It is part of a process in which one envisions a 3D form, thinks of its mathematical representation, writes a program to generate a description of the form, then uses additive freeform technology to physically realize the description. Certain complex structures are most easily realized with a generative program as an intermediate step.

Is a procedurally generated sculpture a sculpture? In what sense?
By definition. (It isn't necessarily a "good" sculpture, but that is an issue independent of the material.) A procedurally generated sculpture can be visually engaging, it can make you think, it can evoke emotions, it can open your imagination to new possibilities, it can delight the senses, it can give you a peek into the mind of the artist who causes it to exist. These are all things one looks for in sculpture.

There seems to me to be less 'intent' and 'expression' than in a traditional sculpture?
I don't think so. To appreciate any genre of art requires some education and alot of individual study. Take my course and I bet you will see more.

You also enjoy mathematical puzzles?
Yes, especially geometric assembly puzzles, which have much in common with my sculpture. But all kinds of puzzles can be fun and serve to open the mind to new directions. They are great for teaching people that there isn't usually a cookbook solution to problems.

Objects need to be 2 manifold to be 3D printed, I've been unable to explain this well to anyone, possibly because I don't understand it. Can you explain it for us?
Not concisely. It often takes a while to understand even when I explain it to my students in class after class.

Four-Dimensional Polytope Projection Barn Raisings, uuum?
They're great fun! I like to organize various kinds of "nerd parties" in which people come together and form a community that creates something cool. Along the way, the professor in me tries to convey a bit of something educational as well. Four-Dimensional Polytope Projection Barn Raisings are one example of that. You can get a sense of them from pictures on my web pages, but you really must attend one to feel the joy of participatory mathematical constructions.

The resulting polytope models seem really beautiful to me, is it because of my natural attraction to symmetry?
It is because they are really beautiful.

Since when have you been involved with rapid prototyping?
I only got even limited access to any machines in the late 1990s.

How did you initially become involved with the technology?
I had an "inside man" who liked making some models for me on the side, as they were cooler than the other jobs he had to do.

What has changed over the years?
The cost is coming down and more people are becoming aware of its incredible power to create any form one can think of. The imagination is now the limiting factor in design, not the hands.

Do you see this as becoming a mass market technology?
I expect that in under ten years there will be machines in service bureaus everywhere, like Kinkos has photocopiers, then every college, then every high school. The types of individuals who now have drill presses or table saws will also have additive fabrication machinery.

Mathematics is of fundamental importance to our society and will only become more important in the future. But, if I look around myself most people I know are turned away from it at a young age. As a teacher, is inspiration an important part of keeping people interested in it? How could more people understand and be interested in math?
It is a shame, because most people never even see any real math to appreciate its beauty. People hate how arithmetic is taught to them in school and, because that is called "math class", they think they hate math.

I love your rhomball model and carry it with me wherever I go. Did you know that in SLS (Selective Laser Sintering or our White, Strong & Flexible material) it bounces very well?
I have an SLS one, about 3 inches in diameter, which I have accidentally dropped a few times. But I usually try not to bounce it, as I can't easily replace my models.

Mathematics and art seem to be polar opposites for some people: one the exact, logical, science, hard truths, the "left brain", the other romantic, creative, expression, "the right brain."Would you agree to this or do you seem them much as part of the same thing?
For thousands of years, people studied math for its beauty. All through history there have been very close connections between art and math. Math is one of the liberal arts. If we taught students to how see the beauty of a theorem or the elegance of a proof they might come at mathematics anew.

You describe Abraham Sharp as an "artist of polyhedra"?
Certainly. My web page about him explains this. Read his book and you will see his love for the beauty of geometry.

Could you explain the "beauty of geometry" to us or do we have to see it?
Can you explain the beauty of the nude human form to us? Appreciating it is just part of being human.

Do you like learning more than teaching?
I think so. But even richer are the pleasures of discovering something new on ones own.