Simplicial Vertex-Normal Duality with Applications to Well-Centered Simplices

  • Jan BrandtsEmail author
  • Michal Křížek
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)


We study the relation between the set of n + 1 vertices of an n-simplex S having \(\mathbb {S}^{n-1}\) as circumsphere, and the set of n + 1 unit outward normals to the facets of S. These normals can in turn be interpreted as the vertices of another simplex \(\hat {S}\) that has \(\mathbb {S}^{n-1}\) as circumsphere. We consider the iterative application of the map that takes the simplex S to \(\hat {S}\), study its convergence properties, and in particular investigate its fixed points. We will also prove some statements about well-centered simplices in the above context.



Michal Křížek was supported by grant no. 18-09628S of the Grant Agency of the Czech Republic.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Korteweg-de Vries Institute for MathematicsUniversity of AmsterdamAmsterdamNetherlands
  2. 2.Institute of MathematicsCzech Academy of SciencesPraha 1Czech Republic

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