Two remarkable movable frameworks (Q1184569)

The author presents an analysis of two overconstrained mechanisms that are both related to regular polyhedra in the Euclidean 3-space. The first one is a modification of Buckminster-Fuller's Jitterbug, called HEUREKA- polyhedron by the author. The second one is called the Grünbaum- framework. It admits at least two types of constrained motions. One has been found by R. Connelly and the other is due to the author (see also the forthcoming Proceeding of the Conference on Intuitive Geometry in Szeged, 1991). These motions are described explicitly.