   too complicated to be written here. Click on the link to download a text file.  X(2), X(4), X(6), X(13), X(14), X(15), X(16), X(30), X(1352), X(2549), X(7735) X(43448) → X(43456) other points below Geometric properties :   K1230 is the pivotal KHO-cubic obtained when the pivot P is the intersection X(43448) of the lines {X2,X99}, {X4,X6}, {X20,X187}, {X30,X1384}, {X32,X3146}, {X39,X3091}, {X76,X2996}, etc, SEARCH = 2.30425578069583. See K1191 for explanations and also CL075. Its KHO-equation is : 2 cotω x y (y - 2 z) + √3 [x^2 (y - z) - z (2 y - z) (y + z)] = 0 where ω is the Brocard angle. Note that [ ... ] = 0 is the cubic K1207. See the analogous cubic K1223.  Other points on K1230 : • Q1 = {4,13} /\ {14,1352} /\ {15,2549} • Q2 = {4,14} /\ {13,1352} /\ {16,2549} • Q3 = {4,15} /\ {13,2549} /\ {16,1352} • Q4 = {4,16} /\ {14,2549} /\ {15,1352} • Q5 on {4,83}, the common tangential of X(4), X(1352), X(2549), SEARCH = 3.24641926939112 • Q6 = {4,1352} /\ {2549,7735} • Q7 = {4,2549} /\ {1352,7735} • Q8 = {1352,2549} /\ {4,7735}   