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

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TL;DR Summary
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.
 
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Fermat point?
 
Thank you for the name. That appears to be correct.
 

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