too complicated to be written here. Click on the link to download a text file. X(2), X(525), X(14846), X(34290) A', B', C' : traces of (L), the trilinear polar of X(1989) other points below
 Q153 is the locus of the radial center X of the stelloidal nK0s. It is analogous to Q004 obtained with stelloidal pKs. Recall that a stelloidal nK0 must have its pole Ω on K396 and its root R on K397. Q153 is a bicircular quintic with triple point G. One tangent at G is parallel to (L) and the two other tangents are real when ABC is obtuse. In this case, these tangents meet (L) at two real points M1, M2 on Q153, on the circum-conic (C) passing through X(1576) which is the transform of (L) under the isoconjugation that swaps X(32) and X(381). Note that the midpoint of M1, M2 is X(51). The following table shows some of these cubics with related points Ω, R and X.
 Ω on K396 X(6) X(523) X(1989) X(9178) X(14560) X(14559) Ω1 Ω3 R on K397 X(6) X(2) X(523) X(5968) X(110) X(14999) X(5967) X(14998) cubic K024 note 1 K205 K1136 K204 X on Q153 X(2) X(14846) X(34290) P0 P2 P1 P3
 note 1 : the cubic splits into the line at infinity and the Kiepert hyperbola. *** Miscellaneous related points P0 = (a^2-a b+b^2-c^2) (a^2+a b+b^2-c^2) (a^2-b^2-a c+c^2) (a^2-b^2+a c+c^2) (a^12-5 a^10 b^2+9 a^8 b^4-8 a^6 b^6+5 a^4 b^8-3 a^2 b^10+b^12-5 a^10 c^2+12 a^8 b^2 c^2-12 a^6 b^4 c^2+6 a^4 b^6 c^2-b^10 c^2+9 a^8 c^4-12 a^6 b^2 c^4+3 a^4 b^4 c^4+b^8 c^4-8 a^6 c^6+6 a^4 b^2 c^6-2 b^6 c^6+5 a^4 c^8+b^4 c^8-3 a^2 c^10-b^2 c^10+c^12) : : , SEARCH = 0.0650713418471199 P1 = (2 a^6-2 a^4 b^2+a^2 b^4-b^6-2 a^4 c^2+b^4 c^2+a^2 c^4+b^2 c^4-c^6) (a^8-a^6 b^2+a^4 b^4+a^2 b^6-2 b^8-a^6 c^2-a^4 b^2 c^2-a^2 b^4 c^2+3 b^6 c^2+a^4 c^4-a^2 b^2 c^4-2 b^4 c^4+a^2 c^6+3 b^2 c^6-2 c^8) : : , SEARCH = 1.20826067234074 P2 = (a^2-a b+b^2-c^2) (a^2+a b+b^2-c^2) (-2 a^2+b^2+c^2) (a^2-b^2-a c+c^2) (a^2-b^2+a c+c^2) (a^16-6 a^14 b^2+11 a^12 b^4-6 a^10 b^6-3 a^8 b^8+6 a^6 b^10-7 a^4 b^12+6 a^2 b^14-2 b^16-6 a^14 c^2+29 a^12 b^2 c^2-49 a^10 b^4 c^2+41 a^8 b^6 c^2-25 a^6 b^8 c^2+20 a^4 b^10 c^2-16 a^2 b^12 c^2+6 b^14 c^2+11 a^12 c^4-49 a^10 b^2 c^4+59 a^8 b^4 c^4-29 a^6 b^6 c^4+11 a^4 b^8 c^4+2 a^2 b^10 c^4-7 b^12 c^4-6 a^10 c^6+41 a^8 b^2 c^6-29 a^6 b^4 c^6-11 a^4 b^6 c^6+5 a^2 b^8 c^6+12 b^10 c^6-3 a^8 c^8-25 a^6 b^2 c^8+11 a^4 b^4 c^8+5 a^2 b^6 c^8-18 b^8 c^8+6 a^6 c^10+20 a^4 b^2 c^10+2 a^2 b^4 c^10+12 b^6 c^10-7 a^4 c^12-16 a^2 b^2 c^12-7 b^4 c^12+6 a^2 c^14+6 b^2 c^14-2 c^16) : : , SEARCH = 0.0701992449232681 P3 = (a^2-a b+b^2-c^2) (a^2+a b+b^2-c^2) (a^2-b^2-a c+c^2) (a^2-b^2+a c+c^2) (a^2 b^2-b^4+a^2 c^2-c^4) (a^18-3 a^16 b^2+6 a^14 b^4-13 a^12 b^6+20 a^10 b^8-21 a^8 b^10+18 a^6 b^12-11 a^4 b^14+3 a^2 b^16-3 a^16 c^2+3 a^14 b^2 c^2+3 a^12 b^4 c^2-8 a^10 b^6 c^2+15 a^8 b^8 c^2-24 a^6 b^10 c^2+24 a^4 b^12 c^2-11 a^2 b^14 c^2+b^16 c^2+6 a^14 c^4+3 a^12 b^2 c^4-9 a^10 b^4 c^4+3 a^8 b^6 c^4+3 a^6 b^8 c^4-18 a^4 b^10 c^4+18 a^2 b^12 c^4-2 b^14 c^4-13 a^12 c^6-8 a^10 b^2 c^6+3 a^8 b^4 c^6+7 a^6 b^6 c^6+5 a^4 b^8 c^6-18 a^2 b^10 c^6+20 a^10 c^8+15 a^8 b^2 c^8+3 a^6 b^4 c^8+5 a^4 b^6 c^8+16 a^2 b^8 c^8+b^10 c^8-21 a^8 c^10-24 a^6 b^2 c^10-18 a^4 b^4 c^10-18 a^2 b^6 c^10+b^8 c^10+18 a^6 c^12+24 a^4 b^2 c^12+18 a^2 b^4 c^12-11 a^4 c^14-11 a^2 b^2 c^14-2 b^4 c^14+3 a^2 c^16+b^2 c^16) : : , SEARCH = 0.172228815586573 Ω1 = (a^4+b^4-a^2 c^2-b^2 c^2) (a^4-a^2 b^2-b^2 c^2+c^4) (2 a^6-2 a^4 b^2+a^2 b^4-b^6-2 a^4 c^2+b^4 c^2+a^2 c^4+b^2 c^4-c^6) : : , SEARCH = 0.615439289833560 Ω3 = a^2 (a^2-a b+b^2-c^2) (a^2+a b+b^2-c^2) (a^2-b^2-a c+c^2) (a^2-b^2+a c+c^2) (a^2 b^2-b^4+a^2 c^2-c^4) (a^6-a^4 b^2-a^2 b^4+b^6-a^4 c^2-b^4 c^2+2 a^2 c^4+2 b^2 c^4-2 c^6) (a^6-a^4 b^2+2 a^2 b^4-2 b^6-a^4 c^2+2 b^4 c^2-a^2 c^4-b^2 c^4+c^6) : : , SEARCH = -0.0828390549533283 These six points above are now in ETC (2019-10-09) as X(34365), X(34366), X(34367), X(34368), X(34369), X(34370). M1 =-3 a^8-3 a^6 b^2+8 a^4 b^4-a^2 b^6-b^8-6 a^4 b^2 c^2+2 a^2 b^4 c^2+2 b^6 c^2+4 a^4 c^4+a^2 b^2 c^4-2 a^2 c^6-2 b^2 c^6+c^8+(a^2-a b+b^2-c^2) (a^2+a b+b^2-c^2) Sqrt[(a^2-b^2-c^2) (a^2+b^2-c^2) (a^2-b^2+c^2) (a^2+b^2+c^2)] : : , SEARCH = -0.466415967914056 M2 =-3 a^8-3 a^6 b^2+8 a^4 b^4-a^2 b^6-b^8-6 a^4 b^2 c^2+2 a^2 b^4 c^2+2 b^6 c^2+4 a^4 c^4+a^2 b^2 c^4-2 a^2 c^6-2 b^2 c^6+c^8-(a^2-a b+b^2-c^2) (a^2+a b+b^2-c^2) Sqrt[(a^2-b^2-c^2) (a^2+b^2-c^2) (a^2-b^2+c^2) (a^2+b^2+c^2)] : : , SEARCH = 0.707667133329048 M1 x M2 = X(34416) = a^4 (a^4+a^2 b^2-2 b^4+a^2 c^2+4 b^2 c^2-2 c^4) : : , SEARCH = -0.0450596653477169