Came up with an answer. After a lot of searching found the angles surrounding point P are all 120 degrees. This made it easier to come up with a geometric description of location.
Question is: Give a geometric description of the location of the Fermat Point that does not involve distance.
How can you do that?
In the diagram below, I have created the Fermat Point.
Definition of Fermat Point: the point such that the sum of its distances from the vertices of a triangle is a minimum.