Trilinears           1/(cos B + cos C) : 1/(cos C + cos A) : 1/(cos A + cos B)
                                    = f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (b + c - a)/(b + c)

Barycentrics    a/(cos B + cos C) : b/(cos C + cos A) : c/(cos A + cos B)

Write I for the incenter; the Euler lines of the four triangles IBC, ICA, IAB, and ABC concur in X(21).

Lev Emelyanov and Tatiana Emelyanova, A note on the Schiffler point, Forum Geometricorum 3 (2003) pages 113-116.

The name of this point honors Kurt Schiffler.

X(21) lies on these lines:
1,31    2,3    6,941    7,56    8,55    9,41    10,35    32,981    36,79    37,172    51,970    60,960    72,943    75,272    77,1394    84,285    90,224    99,105    104,110    107,1295    144,954    145,956    238,256    243,1896    261,314    268,280    270,1172    286,1441    294,1212    332,1036    385,1655    386,1724    517,1389    572,1765    600,1698    612,989    614,988    643,1320    644,1334    662,1156    741,932    748,978    884,885    915,925    961,1402    976,983    1030,1213    1038,1041    1039,1040    1060,1063    1061,1062    1214,1396    1254,1758    1319,1408    1412,1420

X(21) is the {X(2),X(3)}-harmonic conjugate of X(404).

X(21) = midpoint of X(1) and X(191)
X(21) = isogonal conjugate of X(65)
X(21) = isotomic conjugate of X(1441)
X(21) = inverse-in-circumcircle of X(1325)
X(21) = anticomplement of X(442)
X(21) = X(I)-Ceva conjugate of X(J) for these (I,J): (86,81), (261,333)
X(21) = cevapoint of X(I) and X(J) for these (I,J): (1,3), (9,55)

X(21) = X(I)-cross conjugate of X(J) for these (I,J):
(1,29), (3,283), (9,333), (55,284), (58,285), (284,81), (522,100)

X(21) = crosspoint of X(86) and X(333)
X(21) = crosssum of X(I) and X(J) for these (I,J): (1,1046), (42,1400), (1254,1425), (1402,1409)
X(21) = crossdifference of any two points on line X(647)X(661)
X(21) = X(I)-Hirst inverse of X(J) for these (I,J): (2,448), (3,416), (4,425)
X(21) = X(I)-beth conjugate of X(J) for these (I,J): (21,58), (99,21), (643,21), (1043,1043), (1098,21)