Why things don't fall down - Art, geometry and engineering

Why do some geometric shapes hold together, while others are floppy and fall down? An eggshell and a convex dome are rigid, while polygons, with four or more sides of fixed length in the plane, flex. The geometric principles for convex shapes go back to the work in 1813 of A. Cauchy, one of the preeminent mathematicians of the 19th century. More recently a sculptor, Kenneth Snelson, has created many large works, called tensegrities, made of steel struts and cables, where the struts are suspended in mid-air, and yet, when these tensegrities are assembled, they are quite rigid. Why don't these structures fall down? Secrets will be revealed, tensegrity models shown, and participants will be invited to make their own tensegrities from sticks and rubber bands.