Abstract
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.
Dedicated to Sergey Korotov on the occasion of his 50-th birthday.
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Acknowledgements
Michal Křížek was supported by grant no. 18-09628S of the Grant Agency of the Czech Republic.
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Brandts, J., Křížek, M. (2019). Simplicial Vertex-Normal Duality with Applications to Well-Centered Simplices. In: Radu, F., Kumar, K., Berre, I., Nordbotten, J., Pop, I. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2017. ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-96415-7_71
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DOI: https://doi.org/10.1007/978-3-319-96415-7_71
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