From spherical to Euclidean illumination

  • Károly BezdekEmail author
  • Zsolt Lángi


In this note we introduce the problem of illumination of convex bodies in spherical spaces and solve it for a large subfamily of convex bodies. We derive from it a combinatorial version of the classical illumination problem for convex bodies in Euclidean spaces as well as a solution to that for a large subfamily of convex bodies, which in dimension three leads to special Koebe polyhedra.


Spherical space Euclidean space Convex body Illumination number 

Mathematics Subject Classification

52A20 52A55 



We are indebted to the anonymous referee for careful reading and valuable comments.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada
  2. 2.Department of MathematicsUniversity of PannoniaVeszprémHungary
  3. 3.MTA-BME Morphodynamics Research Group and Department of GeometryBudapest University of Technology and EconomicsBudapestHungary

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