3 citations · 3 across the 4 of their papers we have counts for
4 papers · 1 filter
Rigidity of Koebe Polyhedra and Inversive Distance Circle Packings
John C. Bowers, Philip L. Bowers, Carl O. R. Lutz
Hyperbolic inversive distance circle packings on the -sphere correspond to Koebe polyhedra in the Beltrami-Klein model of hyperbolic -space. Koebe polyhedra…
A proof of the Koebe-Andre'ev-Thurston theorem via flow from tangency packings
John C. Bowers
Recently, Connelly and Gortler gave a novel proof of the circle packing theorem for tangency packings by introducing a hybrid combinatorial-geometric operation, flip-and-flow, that…
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 , as well as the infinitesimal inversive rigidity…
Rigidity of Circle Polyhedra in the 2-Sphere and of Hyperideal Polyhedra in Hyperbolic 3-Space
John C. Bowers, Philip L. Bowers, Kevin Pratt
We generalize Cauchy's celebrated theorem on the global rigidity of convex polyhedra in Euclidean -space to the context of circle polyhedra in the -sphere $\…