Trilinears           csc(A - π/3) : csc(B - π/3) : csc(C - π/3)
                                    = sec(A + π/6) : sec(B + π/6) : sec(C + π/6)

Barycentrics    f(a,b,c) : f(b,c,a) : f(c,a,b), where
                                    f(a,b,c) = a⁴ - 2(b² - c²)² + a²(b² + c² - 4*sqrt(3)*Area(ABC))

Construct the equilateral triangle BA'C having base BC and vertex A' on the positive side of BC; similarly construct equilateral triangles CB'A and AC'B based on the other two sides. The lines AA',BB',CC' concur in X(14). The antipedal triangle of X(14) is equilateral.

X(14) lies on these lines:
2,15    3,18    4,62    5,17    6,13    11,203    16,30    76,298    98,383    99,302    148,616    202,1478    226,554    262,1080    275,473    299,533    397,546    484,1276    530,671    532,622    633,636

X(14) is the {X(6),X(381)}-harmonic conjugate of X(13).

X(14) = reflection of X(I) in X(J) for these (I,J): (13,115), (16,395), (99,618), (299,624), (617,619)
X(14) = isogonal conjugate of X(16)
X(14) = isotomic conjugate of X(299)
X(14) = inverse-in-orthocentroidal-circle of X(13)
X(14) = complement of X(617)
X(14) = anticomplement of X(619)
X(14) = cevapoint of X(16) and X(61)
X(14) = X(I)-cross conjugate of X(J) for these (I,J): (16,17), (30,13), (395,2)