Some remarks on the geometry of contact formation cells

The contact formation cells of a polygonal planar system of rigid bodies in contact have been studied in Farahat et al. There, it was shown that the CF-cells are smooth manifolds, but the methods used were too complicated to extend to three-dimensional polygonal rigid body systems. In this paper, the authors develop an alternative way to define contact formation cells. Under the new definition, the authors show that the contact formation cells are smooth manifolds, and further that all intersections of contact formation cells are smooth manifolds. The simplicity of the new definition makes it easy to prove the smoothness results for three-dimensional systems. Also, the authors investigate other extensions of the results in Farahat et al