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Coincidences of simplex centers and related facial structures

Allan L. Edmonds·Mowaffaq Hajja·Horst Martini
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Abstract

We investigate the geometric properties of simplices in Euclidean d-dimensional space for which two or more of the analogues of the classical triangle centers (including the centroid, circumcenter, incenter, orthocenter or Monge point, and the Fermat-Torricelli point) coincide. We also investigate the geometric significance of the cevian line segments through a given center having the same length. We give a unified presentation, including known results for d=2 and d=3.

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Allan L. Edmonds, Mowaffaq Hajja, Horst Martini. 2004-11-04. Coincidences of simplex centers and related facial structures. https://arxiv.org/abs/math/0411093

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