Trilinears           cos A - 2 cos B cos C : cos B - 2 cos C cos A : cos C - 2 cos A cos B
                                    = f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = bc[2a⁴ - (b² - c²)² - a²(b² + c²)]

Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = 2a⁴ - (b² - c²)² - a²(b² + c²)

X(30) is the point of intersection of the Euler line and the line at infinity. Thus, each of the 41 lines listed below is parallel to the Euler line.

X(30) lies on these lines:
1,79    2,3    11,36    12,35    13,15    14,16    33,1060    34,1062    40,191    46,1837    49,1614    52,185    53,577    55,495    56,496    58,1834    61,397    62,398    64,68    65,1770    74,265    80,484    98,671    99,316    104,1290    110,477    113,1495    115,187    143,389    146,323    148,385    155,1498    156,1147    182,597    262,598    284,1901    298,616    299,617    340,1494    390,1056    485,1151    486,1152    489,638    490,637    497,999    511,512    551,946    553,942    582,1724    599,1350    618,623    619,624    620,625    841,1302    935,1297    944,962    1043,1330    1141,1157    1155,1737    1294,1304    1319,1387    1351,1353    1465,1877    1838,1852

X(30) = orthopoint of X(523)
X(30) = isogonal conjugate of X(74)
X(30) = isotomic conjugate of X(1494)
X(30) = anticomplementary conjugate of X(146)
X(30) = complementary conjugate of X(113)
X(30) = X(I)-Ceva conjugate of X(J) for these (I,J): (4,113), (265,5), (476,523)
X(30) = cevapoint of X(3) and X(399)
X(30) = crosspoint of X(I) and X(J) for these (I,J): (13,14), (94,264)
X(30) = crosssum of X(I) and X(J) for these (I,J): (15,16), (50,184)
X(30) = crossdifference of any two points on line X(6)X(647)