Almost all circle polyhedra are rigid
John C. Bowers, Philip L. Bowers, Kevin Pratt
We verify the infinitesimal inversive rigidity of almost all triangulated circle polyhedra in the Euclidean plane E^2, as well as the infinitesimal inversive rigidity of tangency circle packings on the 2-sphere S^2. From this the rigidity of almost all triangulated circle polyhedra follows. The proof adapts Gluck's proof in  of the rigidity of almost all Euclidean polyhedra to the setting of circle polyhedra, where inversive distances replace Euclidean distances and Moebius transformations replace rigid Euclidean motions.