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Pods are mechanical devices constituted of two rigid bodies, the base and the platform, connected by a number of other rigid bodies, called legs, that are anchored via spherical joints. It is possible to prove that the maximal number of legs of a mobile pod, when finite, is 20. In 1904, Borel designed a technique to construct examples of such 20-pods. We show that recent results about spectrahedra provide a way to determine solutions for Borel’s construction with all real coordinates.
This is a joint work with Georg Nawratil, Jon Selig, and Josef Schicho.