Dali's horse project never got too far. He kept changing the parameters of the problem, and it became more and more unrealistic. But the principles behind the computer exercise were clear enough from the beginning, and it surprises me now to realize how much trouble we had with them then. Maybe it's time to go back and do the project over, at least in a rudimentary form.
Can you find the exact reference in The Fountainhead and carry a bit further your suggestion that it might be different if clay manipulation were replaced by interactive computer graphics? By the way, to italicize, put "bracket i" before and "bracket slash i" afterwards.
Figuring out something like the projections of a tennis ball curve is definitely a good exercise. It can work backwards too, when a student tries to figure out what kind of curve on the sphere could cast an elliptical image, or a square.
My understanding is that the word "tesseract" comes either from the word for "tile" as in a piece of a mosaic in a tesselation, or it derives from a form of the Greek numeral "tetra". In either case, you get a four-dimensional building block so the dual etymology works.
We should do some computer demonstration of the way the polyhedral torus behaves as we rotate in three- and four-dimensional space. That is the best way of showing what is happening, in my opinion. You can ask me about it if I don't get to it by Wednesday afternoon.