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Mathematics and Statistics
Completed Project

Tensegrity: Theory and Practice

Nicolas Demaria ’21, Matthew Goldberg ’20, and Professor John McCleary

We have studied the mathematics of tensegrities through a survey of tensegrity literature and construction projects. We developed several construction methodologies, and explored their value in informal education.  Tensegrities can be understood as interactions between truss-cable reductions of polyhedra. When first observing a tensegrity, one is struck by its counterintuitive design and seemingly brittle appearance. Then, when one touches the structure, its rigidity becomes instantly apparent. Finally, when building a tensegrity, we became acquainted with the beautiful, idiosyncratic language of tensegrity design. Many of the symmetries from the structures’ antecedents are preserved in this process, and can even be understood algebraically. These symmetries can then be exploited in their construction. For example, when making the extended octahedron, we used the symmetries of the vertices to approach the construction modularly. We explored an array of different materials and came up with our own methods to streamline construction. One can also observe that many larger tensegrities are composed of smaller tensegrities, seeming to suggest that there exist a number of irreducible, rigid structures that act as irreducible elements through all tensegrities. Studies in tensegrity structures offer an exciting opportunity to introduce mathematical principles and structural design in an informal and highly tactile setting. The continuous tension structures are visually engaging and seem to defy our innate structural intuitions. This spark of curiosity can then be transferred into creativity in one’s own construction projects. The study of tensegrities joins design and mathematics in an elegant, comprehensive union.