## X(3122) (DANNEELS PERSPECTOR FOR X(42))

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears            f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a(b + c)(b - c)2
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(3122) lies on these lines:
6,2054    11,244    86,256    190,291    351,865    674,3009    1400,1918    1929,2640    2092,2667    2110,2277    2642,2643

X(3122) = X(I)-Ceva conjugate of X(J) for these I,J: 10,661    42,512    58,649    244,3125    256,513    310,514    1015,3121    1400,798    1474,1919

X(3122) = X(3124)-cross conjugate of X(3125)
X(3122) = crosspoint of X(I) and X(J) for these I,J: 10,661    37,513    42,512    58,649    244,1015    310,514    667,1402
X(3122) = crosssum of X(I) and X(J) for these I,J: 10,190    58,662    81,100    86,99    101,1918    306,1331    314,668    333,643    645,1043    765,1016    1332,1792

X(3122) = crossdifference of every pair of points on the line X(99)X(101)

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.