Abstract
The rigidity theorems of Alexandrov (1950) and Stoker (1968) are classical results in the theory of convex polyhedra. We prove analogues of them for ball-polyhedra, which are intersections of finitely many congruent balls in Euclidean 3-space.
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References
Aigner, M., Ziegler, G.M.: Proofs from The Book, 4th edn. Springer, Berlin (2010)
Aurenhammer, F., Klein, R.: Voronoi Diagrams. In: Handbook of Computational Geometry, pp. 201–290. North-Holland, Amsterdam (2000)
Alexandrov, A.D.: Convex Polyhedra. Springer, Berlin (2005)
Bezdek, K., Naszódi, M.: Rigidity of Ball-Polyhedra in Euclidean 3-Space. European J. Combin. 27(2), 255–268 (2005)
Bezdek, K., Lángi, Z., Naszódi, M., Papez, P.: Ball-Polyhedra. Discrete Comput. Geom. 38(2), 201–230 (2007)
Bezdek, K.: Classical Topics in Discrete Geometry. CMS Books in Mathematics. Springer, New York (2010)
Bezdek, K., Naszódi, M.: Rigid Ball-polyhedra in Euclidean 3-Space. Discrete Comput. Geom., 1–14 (to appear)
Cauchy, A.L.: Sur les polygones et polyèdres, Second mémoire. J. de l’Ecole Polythéchnique 9, 87–98 (1813)
Edelsbrunner, H., Kirkpatrick, D.G., Seidel, R.: On the Shape of a Set of Points in the Plane. IEEE Trans. Inform. Theory 29(4), 551–559 (1983)
Kupitz, Y.S., Martini, H., Perles, M.A.: Ball Polytopes and the Vázsonyi Problem. Acta Math. Hungar. 126(1-2), 99–163 (2010)
Pak, I.: Lectures on Discrete and Polyhedral Geometry, 1–440 (2010), http://www.math.ucla.edu/~pak/geompol8.pdf,
Sabitov, I.K.: Around the Proof of the Legendre-Cauchy Lemma on Convex Polygons. Siberian Math. J. 45(4), 740–762 (2004)
Seidel, R.: Exact Upper Bounds for the Number of Faces in d-Dimensional Voronoi Diagrams. DIMACS Ser. Discrete Math. Theoret. Comput. Sci., Amer. Math. Soc., Applied Geometry and Discrete Mathematics 4, 517–529 (1991)
Stoker, J.J.: Geometric Problems Concerning Polyhedra in the Large. Com. Pure and Applied Math. 21, 119–168 (1968)
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Bezdek, K. (2013). Globally Rigid Ball-Polyhedra in Euclidean 3-Space. In: Gavrilova, M.L., Tan, C.J.K., Kalantari, B. (eds) Transactions on Computational Science XX. Lecture Notes in Computer Science, vol 8110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41905-8_10
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DOI: https://doi.org/10.1007/978-3-642-41905-8_10
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