Significance of Equal Angle Triangle Center

Question

While playing around with triangle centers and came across one I did not know, the center where each triangle corner heading is equally spaced ($120^\circ$ spacing).

Does this specific triangle center have a name, and does it have any significance?

Answer 1

This is the first isogonic centre (Kimberling $X_{13}$), which in a triangle whose angles are all less than $120^\circ$ is also the Fermat point, i.e. minimises the sum of distances to the three vertices or solves the Steiner problem for the triangle.

For a triangle with an angle at least $120^\circ$, the Fermat point is exactly on the corresponding vertex.