What is the name of the triangle centre point with 120° subtended vertices?

[Baluncore]

TL;DR

There are a couple of thousand definitions for different triangle centres.

I am looking for the name of the triangle centre point from which the vertices subtend 120°.

I am concerned really with deviant equilateral triangles, thru to right angle triangles. Flat triangles, that have an internal angle greater than 120°, do not have such a point within the triangle.

The lines from that centre point to the three vertices is the minimum total line length needed to connect the vertices.

 

[pbuk]

Fermat point?

 

[Baluncore]

Thank you for the name. That appears to be correct.