Here's a hyperboloid I made out of kabob skewers and rubber bands. It is largely reminiscent of this awesome double napped cone made out of string one of my math teachers had in his room. Anyhow, the hyperboloid is the surface obtained by revolving a hyperbola about its semi minor axis. It sits nestled around a jar here so that I could take a picture of it, but it's an awful lot of fun to play with - stretching/pushing it flatter and watching it change, giving the whole thing more curve by moving the rubber bands closer together, etc. It also makes a great hat. I like this construction because it illustrates the doubly ruled nature of the hyperboloid - that through every point, there are two distinct lines that pass through it on the surface.
An alternate view
I like how it looks from the top - like some 12 pointed star or something.
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