Two points closely related to the Napoleon points are the Fermat-Torricelli points (ETC's X13 and X14). If instead of constructing lines joining the equilateral triangles' centroids to the respective vertices one now constructs lines joining the equilateral triangles' apices to the respective vertices of the triangle, the three lines so constructed are again concurrent. The points of concurrence are called the Fermat-Torricelli points, sometimes denoted F1 and F2. The intersection of the Fermat line (i.e., that line joining the two Fermat-Torricelli points) and the Napoleon line (i.e., that line joining the two Napoleon points) is the triangle's symmedian point (ETC's X6).
