The hexyl circle is the circumcircle of the hexyl triangle. Amazingly, its center is at the incenter I and its radius is 2R, where R is the circumradius. Its circle function is l = - (a^4 - 2b a^3 - 2c a^3 + 2b^3 a + 2c^3 a - 2b c^2 a - 2b^2 c a - b^4 - c^4 + 2b^2 c^2)/(4Δ^2), where Δ is the area of the reference triangle, which is not a Kimberling center. No Kimberling centers lie on it.

central circle | hexyl triangle