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Globally Rigid Ball-Polyhedra in Euclidean 3-Space

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Book cover Transactions on Computational Science XX

Part of the book series: Lecture Notes in Computer Science ((TCOMPUTATSCIE,volume 8110))

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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

  1. Aigner, M., Ziegler, G.M.: Proofs from The Book, 4th edn. Springer, Berlin (2010)

    Book  Google Scholar 

  2. Aurenhammer, F., Klein, R.: Voronoi Diagrams. In: Handbook of Computational Geometry, pp. 201–290. North-Holland, Amsterdam (2000)

    Chapter  Google Scholar 

  3. Alexandrov, A.D.: Convex Polyhedra. Springer, Berlin (2005)

    MATH  Google Scholar 

  4. Bezdek, K., Naszódi, M.: Rigidity of Ball-Polyhedra in Euclidean 3-Space. European J. Combin. 27(2), 255–268 (2005)

    Article  Google Scholar 

  5. Bezdek, K., Lángi, Z., Naszódi, M., Papez, P.: Ball-Polyhedra. Discrete Comput. Geom. 38(2), 201–230 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bezdek, K.: Classical Topics in Discrete Geometry. CMS Books in Mathematics. Springer, New York (2010)

    Book  MATH  Google Scholar 

  7. Bezdek, K., Naszódi, M.: Rigid Ball-polyhedra in Euclidean 3-Space. Discrete Comput. Geom., 1–14 (to appear)

    Google Scholar 

  8. Cauchy, A.L.: Sur les polygones et polyèdres, Second mémoire. J. de l’Ecole Polythéchnique 9, 87–98 (1813)

    Google Scholar 

  9. 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)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kupitz, Y.S., Martini, H., Perles, M.A.: Ball Polytopes and the Vázsonyi Problem. Acta Math. Hungar. 126(1-2), 99–163 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Pak, I.: Lectures on Discrete and Polyhedral Geometry, 1–440 (2010), http://www.math.ucla.edu/~pak/geompol8.pdf,

  12. Sabitov, I.K.: Around the Proof of the Legendre-Cauchy Lemma on Convex Polygons. Siberian Math. J. 45(4), 740–762 (2004)

    Article  MathSciNet  Google Scholar 

  13. 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)

    MathSciNet  Google Scholar 

  14. Stoker, J.J.: Geometric Problems Concerning Polyhedra in the Large. Com. Pure and Applied Math. 21, 119–168 (1968)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Calgary, Canada

    Károly Bezdek

  2. Department of Mathematics, University of Pannonia, Veszprém, Hungary

    Károly Bezdek

Authors
  1. Károly Bezdek
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Editor information

Editors and Affiliations

  1. University of Calgary, Calgary, AB, Canada

    Marina L. Gavrilova

  2. CloudFabriQ Ltd., Warnford Court, 29 Throgmorton Street, EC2N 2AT, London, UK

    C. J. Kenneth Tan

  3. Rutgers University, New Brunswick, NJ, USA

    Bahman Kalantari

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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

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41904-1

  • Online ISBN: 978-3-642-41905-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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