too complicated to be written here. Click on the link to download a text file. X(1), X(2), X(3), X(4), X(6), X(7), X(354), X(672), X(955), X(991), X(5728), X(14547), X(14548), X(14549) other points below
 K382 is the only (undecomposed) cubic passing through I, G, O, H, K and Ge (Gergonne point) i.e. six centers of the ETC Top 10. See also K696 and Table 30. The following table gives alignments and other points on the cubic.
 Xi Xj Xk / pt notes/1st baryc. Search 1 2 1 G is the tangential of I * 1 3 354 * 1 4 14547 * 1 6 5728 * 1 7 991 * 1 672 a*(a^4*b - a^3*b^2 - a^2*b^3 + a*b^4 + a^4*c + a^3*b*c - 2*a^2*b^2*c - a*b^3*c + b^4*c - a^3*c^2 - 2*a^2*b*c^2 - 4*a*b^2*c^2 - b^3*c^2 - a^2*c^3 - a*b*c^3 - b^2*c^3 + a*c^4 + b*c^4)/(2*b*c + a*b + a*c - a^2) 1.5149423271 1 995 ugly 0.39759327634 2 3 4 * 2 6 14548 * 2 7 672 * 2 354 a(a^2+b^2+c^2-2*a*b-2*a*c)/(-a^2+a*b+a*c+2*b*c) -0.26879818663 2 955 5728 * 2 991 1/(a^4 - a^3*b - a^2*b^2 + a*b^3 - a^3*c - a^2*b*c + a*b^2*c + b^3*c - a^2*c^2 + a*b*c^2 - 2*b^2*c^2 + a*c^3 + b*c^3) 6.1661934751 3 6 991 * 3 7 OGe (3*a^2*b-2*a*b^2-b^3+3*a^2*c+4*a*b*c+b^2*c-2*a*c^2+b*c^2-c^3)/(a^2*b-b^3+a^2*c+2*a*b*c+b^2*c+b*c^2-c^3) 1.8270354007 3 672 a^2(a*b+a*c-b^2-c^2)/(-a^3+a^2*b-a*b^2+b^3+a^2*c-2*a*b*c-b^2*c-a*c^2-b*c^2+c^3) -12.113065373 3 955 ugly 1.794898451968 4 6 HK ugly -31.019596589 4 7 5728 * 4 354 ugly 1.533666290999 4 672 ugly -4.8466314073 4 955 ugly 1.198832957781 4 991 14549 * 6 7 ugly 2.4103172619 6 354 a*(a^5 - a^4*b - a*b^4 + b^5 - a^4*c - 2*a^3*b*c + 2*a^2*b^2*c + 2*a*b^3*c - b^4*c + 2*a^2*b*c^2 + 6*a*b^2*c^2 + 2*a*b*c^3 - a*c^4 - b*c^4 + c^5)/(a^2 + b^2 + c^2 - 2*a*b - 2*a*c) 18.74219943685 6 672 14547 * 6 955 ugly 1.769623144772 7 354 14548 * 7 955 ugly -0.4068239559082 354 672 14549 * 354 955 HK ugly -31.019596589 354 991 a^2*(a^2 - b^2 - 4*b*c - c^2)/(-a^5 + 2*a^4*b - 2*a^2*b^3 + a*b^4 + 2*a^4*c + 2*a^3*b*c - 5*a^2*b^2*c + b^4*c - 5*a^2*b*c^2 - 2*a*b^2*c^2 - b^3*c^2 - 2*a^2*c^3 - b^2*c^3 + a*c^4 + b*c^4) 1.658226689587 672 955 ugly 1.664615036028 672 991 ugly -0.880651271322 955 991 14547 *