Isogonic and isodynamic points of a simplex in a real affine space

Abstract

A non-equilateral triangle in a Euclidean plane has exactly two isogonic and two isodynamic points. There are a number of different but equivalent characterizations of these triangle centers. The aim of this paper is to work out characteristic properties of isogonic and isodynamic centers of simplices that can be transferred to higher dimensions. In addition, a geometric description of the Weiszfeld algorithm for calculating the Fermat point of a simplex is given.