Trilinears           f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a³[b⁸ + c⁸ - a⁸ - 2a²(b⁶ + c⁶)
                                    + 2b²c²(b⁴ + c⁴ - 5a⁴ + 3a²b² + 3a²c² - 3b²c²) + 2a⁶(b² + c²)]

Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

Let A_b be the point in which the line through A perpendicular to CA meets line BC, and define points A_c, B_c, B_a, C_a, C_b functionally. Let

X_a = midpoint{A_b, A_c},
Y_a = midpoint{B_a, C_a},
Z_a = midpoint{B_c, C_b},

and define X_b, X_c, Y_b, Y_c, Z_b, Z_c functionally.

The lines AX_a, BX_b, CX_c concur in X(20).
The lines AY_a, BY_b, CY_c concur in X(393).
The lines AZ_a, BZ_b, CZ_c concur in X(6).
The lines X_aY_a, X_bY_b, X_cY_c concur in X(1660).
The lines Y_aZ_a, Y_bZ_b, Y_cZ_c concur in X(3).
The lines Z_aX_a, Z_bX_b, Z_cX_c concur in X(1661).

Contributed by Darij Grinberg, August 24, 2003; see Hyacinthos #7225.

X(1660) lies on these lines: 6,25    30,156    110,1370    394,1619    578,1596    1092,1498    1368,1503

X(1660) = midpoint of X(394) and X(1619)
X(1660) = X(20)-Ceva conjugate of X(577)