Discrete & Computational Geometry

, Volume 60, Issue 1, pp 9–26 | Cite as

Ma–Schlenker c-Octahedra in the 2-Sphere

  • John C.  BowersEmail author
  • Philip L.  Bowers


We present constructions inspired by the Ma–Schlenker example of “Non-rigidity of spherical inversive distance circle packings” (Discrete Comput Geom 47(3):610–617, 2012). In contrast to the use in Ma and Schlenker (2012) of an infinitesimally flexible Euclidean polyhedron, embeddings in de Sitter space, and Pogorelov maps, our elementary constructions use only the inversive geometry of the 2-sphere.


Inversive geometry Circle packing Circle octahedra 

Mathematics Subject Classification



  1. 1.
    Bowers, P.L., Hurdal, M.K.: Planar conformal mappings of piecewise flat surfaces. In: Hege, H.-C., Polthier, K. (eds.) Visualization and Mathematics III, Chapter 1, pp. 3–34. Springer, Berlin (2003)CrossRefGoogle Scholar
  2. 2.
    Bowers, P.L., Stephenson, K.: Uniformizing dessins and Belyĭ maps via circle packing. Mem. Am. Math. Soc. 170(805), 1–97 (2004)zbMATHGoogle Scholar
  3. 3.
    Guo, R.: Local rigidity of inversive distance circle packing. Trans. Am. Math. Soc. 363(9), 4757–4776 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Luo, F.: Rigidity of polyhedral surfaces, III. Geom. Topol. 15(4), 2299–2319 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Ma, J., Schlenker, J.-M.: Non-rigidity of spherical inversive distance circle packings. Discrete Comput. Geom. 47(3), 610–617 (2012)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceJames Madison UniversityHarrisonburgUSA
  2. 2.Department of MathematicsThe Florida State UniversityTallahasseeUSA

Personalised recommendations