The first Fermat point F1 of a triangle ABC is the perspective center between ABC and the triangle having as vertices the vertices added to the external Fermat triangles of ABC.
The second Fermat point F2 of a triangle ABC is the perspective center between ABC and the triangle having as vertices the vertices added to the internal Fermat triangles of ABC.
They are also called isogonic points. They are the points X(13) and X(14) in ETC.