http://amontes.webs.ull.es/otrashtm/HGT2017.htm#HG280217

Dado un triángulo ABC y un punto P, sea A'B'C' el triángulo antipedal de P.

La paralela por C' a AP interseca a BC en Ab y la paralela por B' a AP interseca a BC en Ac. Los puntos Bc, Ba, Ca y Cb se definen cíclicamente.


Los seis puntos Ab, Ac,  Bc, Ba, Ca y Cb están sobre una cónica si P está sobre una nónica circunscrita a ABC y al triángulo excentral y que pasa por el incentro y el punto de De Longchamps, de ecuación:
 

-4 a^6 c^6 x^6 y^3-12 a^4 b^2 c^6 x^6 y^3-12 a^2 b^4 c^6 x^6 y^3+28 b^6 c^6 x^6 y^3+12 a^4 c^8 x^6 y^3+24 a^2 b^2 c^8 x^6 y^3-20 b^4 c^8 x^6 y^3-12 a^2 c^10 x^6 y^3-12 b^2 c^10 x^6 y^3+4 c^12 x^6 y^3-24 a^6 c^6 x^5 y^4-48 a^4 b^2 c^6 x^5 y^4+24 a^2 b^4 c^6 x^5 y^4+48 b^6 c^6 x^5 y^4+56 a^4 c^8 x^5 y^4+32 a^2 b^2 c^8 x^5 y^4-72 b^4 c^8 x^5 y^4-40 a^2 c^10 x^5 y^4+16 b^2 c^10 x^5 y^4+8 c^12 x^5 y^4-48 a^6 c^6 x^4 y^5-24 a^4 b^2 c^6 x^4 y^5+48 a^2 b^4 c^6 x^4 y^5+24 b^6 c^6 x^4 y^5+72 a^4 c^8 x^4 y^5-32 a^2 b^2 c^8 x^4 y^5-56 b^4 c^8 x^4 y^5-16 a^2 c^10 x^4 y^5+40 b^2 c^10 x^4 y^5-8 c^12 x^4 y^5-28 a^6 c^6 x^3 y^6+12 a^4 b^2 c^6 x^3 y^6+12 a^2 b^4 c^6 x^3 y^6+4 b^6 c^6 x^3 y^6+20 a^4 c^8 x^3 y^6-24 a^2 b^2 c^8 x^3 y^6-12 b^4 c^8 x^3 y^6+12 a^2 c^10 x^3 y^6+12 b^2 c^10 x^3 y^6-4 c^12 x^3 y^6+a^10 c^2 x^6 y^2 z+a^8 b^2 c^2 x^6 y^2 z-2 a^6 b^4 c^2 x^6 y^2 z-10 a^4 b^6 c^2 x^6 y^2 z+17 a^2 b^8 c^2 x^6 y^2 z-7 b^10 c^2 x^6 y^2 z-a^8 c^4 x^6 y^2 z+4 a^6 b^2 c^4 x^6 y^2 z+6 a^4 b^4 c^4 x^6 y^2 z-52 a^2 b^6 c^4 x^6 y^2 z+43 b^8 c^4 x^6 y^2 z-6 a^6 c^6 x^6 y^2 z-10 a^4 b^2 c^6 x^6 y^2 z+42 a^2 b^4 c^6 x^6 y^2 z+38 b^6 c^6 x^6 y^2 z+14 a^4 c^8 x^6 y^2 z+4 a^2 b^2 c^8 x^6 y^2 z-78 b^4 c^8 x^6 y^2 z-11 a^2 c^10 x^6 y^2 z+b^2 c^10 x^6 y^2 z+3 c^12 x^6 y^2 z+7 a^10 c^2 x^5 y^3 z+a^8 b^2 c^2 x^5 y^3 z-26 a^6 b^4 c^2 x^5 y^3 z+2 a^4 b^6 c^2 x^5 y^3 z+35 a^2 b^8 c^2 x^5 y^3 z-19 b^10 c^2 x^5 y^3 z-9 a^8 c^4 x^5 y^3 z+12 a^6 b^2 c^4 x^5 y^3 z-54 a^4 b^4 c^4 x^5 y^3 z-20 a^2 b^6 c^4 x^5 y^3 z+71 b^8 c^4 x^5 y^3 z-30 a^6 c^6 x^5 y^3 z-6 a^4 b^2 c^6 x^5 y^3 z+118 a^2 b^4 c^6 x^5 y^3 z+46 b^6 c^6 x^5 y^3 z+74 a^4 c^8 x^5 y^3 z-44 a^2 b^2 c^8 x^5 y^3 z-150 b^4 c^8 x^5 y^3 z-57 a^2 c^10 x^5 y^3 z+37 b^2 c^10 x^5 y^3 z+15 c^12 x^5 y^3 z+18 a^10 c^2 x^4 y^4 z-18 a^8 b^2 c^2 x^4 y^4 z-36 a^6 b^4 c^2 x^4 y^4 z+36 a^4 b^6 c^2 x^4 y^4 z+18 a^2 b^8 c^2 x^4 y^4 z-18 b^10 c^2 x^4 y^4 z-36 a^8 c^4 x^4 y^4 z-24 a^6 b^2 c^4 x^4 y^4 z+24 a^2 b^6 c^4 x^4 y^4 z+36 b^8 c^4 x^4 y^4 z-48 a^6 c^6 x^4 y^4 z-24 a^4 b^2 c^6 x^4 y^4 z+24 a^2 b^4 c^6 x^4 y^4 z+48 b^6 c^6 x^4 y^4 z+132 a^4 c^8 x^4 y^4 z-132 b^4 c^8 x^4 y^4 z-66 a^2 c^10 x^4 y^4 z+66 b^2 c^10 x^4 y^4 z+19 a^10 c^2 x^3 y^5 z-35 a^8 b^2 c^2 x^3 y^5 z-2 a^6 b^4 c^2 x^3 y^5 z+26 a^4 b^6 c^2 x^3 y^5 z-a^2 b^8 c^2 x^3 y^5 z-7 b^10 c^2 x^3 y^5 z-71 a^8 c^4 x^3 y^5 z+20 a^6 b^2 c^4 x^3 y^5 z+54 a^4 b^4 c^4 x^3 y^5 z-12 a^2 b^6 c^4 x^3 y^5 z+9 b^8 c^4 x^3 y^5 z-46 a^6 c^6 x^3 y^5 z-118 a^4 b^2 c^6 x^3 y^5 z+6 a^2 b^4 c^6 x^3 y^5 z+30 b^6 c^6 x^3 y^5 z+150 a^4 c^8 x^3 y^5 z+44 a^2 b^2 c^8 x^3 y^5 z-74 b^4 c^8 x^3 y^5 z-37 a^2 c^10 x^3 y^5 z+57 b^2 c^10 x^3 y^5 z-15 c^12 x^3 y^5 z+7 a^10 c^2 x^2 y^6 z-17 a^8 b^2 c^2 x^2 y^6 z+10 a^6 b^4 c^2 x^2 y^6 z+2 a^4 b^6 c^2 x^2 y^6 z-a^2 b^8 c^2 x^2 y^6 z-b^10 c^2 x^2 y^6 z-43 a^8 c^4 x^2 y^6 z+52 a^6 b^2 c^4 x^2 y^6 z-6 a^4 b^4 c^4 x^2 y^6 z-4 a^2 b^6 c^4 x^2 y^6 z+b^8 c^4 x^2 y^6 z-38 a^6 c^6 x^2 y^6 z-42 a^4 b^2 c^6 x^2 y^6 z+10 a^2 b^4 c^6 x^2 y^6 z+6 b^6 c^6 x^2 y^6 z+78 a^4 c^8 x^2 y^6 z-4 a^2 b^2 c^8 x^2 y^6 z-14 b^4 c^8 x^2 y^6 z-a^2 c^10 x^2 y^6 z+11 b^2 c^10 x^2 y^6 z-3 c^12 x^2 y^6 z-a^10 b^2 x^6 y z^2+a^8 b^4 x^6 y z^2+6 a^6 b^6 x^6 y z^2-14 a^4 b^8 x^6 y z^2+11 a^2 b^10 x^6 y z^2-3 b^12 x^6 y z^2-a^8 b^2 c^2 x^6 y z^2-4 a^6 b^4 c^2 x^6 y z^2+10 a^4 b^6 c^2 x^6 y z^2-4 a^2 b^8 c^2 x^6 y z^2-b^10 c^2 x^6 y z^2+2 a^6 b^2 c^4 x^6 y z^2-6 a^4 b^4 c^4 x^6 y z^2-42 a^2 b^6 c^4 x^6 y z^2+78 b^8 c^4 x^6 y z^2+10 a^4 b^2 c^6 x^6 y z^2+52 a^2 b^4 c^6 x^6 y z^2-38 b^6 c^6 x^6 y z^2-17 a^2 b^2 c^8 x^6 y z^2-43 b^4 c^8 x^6 y z^2+7 b^2 c^10 x^6 y z^2-5 a^10 b^2 x^5 y^2 z^2+13 a^8 b^4 x^5 y^2 z^2-2 a^6 b^6 x^5 y^2 z^2-22 a^4 b^8 x^5 y^2 z^2+23 a^2 b^10 x^5 y^2 z^2-7 b^12 x^5 y^2 z^2+5 a^10 c^2 x^5 y^2 z^2-14 a^6 b^4 c^2 x^5 y^2 z^2-32 a^4 b^6 c^2 x^5 y^2 z^2+81 a^2 b^8 c^2 x^5 y^2 z^2-40 b^10 c^2 x^5 y^2 z^2-13 a^8 c^4 x^5 y^2 z^2+14 a^6 b^2 c^4 x^5 y^2 z^2-54 a^2 b^6 c^4 x^5 y^2 z^2+149 b^8 c^4 x^5 y^2 z^2+2 a^6 c^6 x^5 y^2 z^2+32 a^4 b^2 c^6 x^5 y^2 z^2+54 a^2 b^4 c^6 x^5 y^2 z^2+22 a^4 c^8 x^5 y^2 z^2-81 a^2 b^2 c^8 x^5 y^2 z^2-149 b^4 c^8 x^5 y^2 z^2-23 a^2 c^10 x^5 y^2 z^2+40 b^2 c^10 x^5 y^2 z^2+7 c^12 x^5 y^2 z^2+a^12 x^4 y^3 z^2-8 a^10 b^2 x^4 y^3 z^2+17 a^8 b^4 x^4 y^3 z^2-8 a^6 b^6 x^4 y^3 z^2-13 a^4 b^8 x^4 y^3 z^2+16 a^2 b^10 x^4 y^3 z^2-5 b^12 x^4 y^3 z^2+31 a^10 c^2 x^4 y^3 z^2-a^8 b^2 c^2 x^4 y^3 z^2-134 a^6 b^4 c^2 x^4 y^3 z^2+82 a^4 b^6 c^2 x^4 y^3 z^2+87 a^2 b^8 c^2 x^4 y^3 z^2-65 b^10 c^2 x^4 y^3 z^2-70 a^8 c^4 x^4 y^3 z^2+80 a^6 b^2 c^4 x^4 y^3 z^2+48 a^4 b^4 c^4 x^4 y^3 z^2-136 a^2 b^6 c^4 x^4 y^3 z^2+142 b^8 c^4 x^4 y^3 z^2+2 a^6 c^6 x^4 y^3 z^2-110 a^4 b^2 c^6 x^4 y^3 z^2+138 a^2 b^4 c^6 x^4 y^3 z^2+34 b^6 c^6 x^4 y^3 z^2+89 a^4 c^8 x^4 y^3 z^2-40 a^2 b^2 c^8 x^4 y^3 z^2-197 b^4 c^8 x^4 y^3 z^2-65 a^2 c^10 x^4 y^3 z^2+79 b^2 c^10 x^4 y^3 z^2+12 c^12 x^4 y^3 z^2+5 a^12 x^3 y^4 z^2-16 a^10 b^2 x^3 y^4 z^2+13 a^8 b^4 x^3 y^4 z^2+8 a^6 b^6 x^3 y^4 z^2-17 a^4 b^8 x^3 y^4 z^2+8 a^2 b^10 x^3 y^4 z^2-b^12 x^3 y^4 z^2+65 a^10 c^2 x^3 y^4 z^2-87 a^8 b^2 c^2 x^3 y^4 z^2-82 a^6 b^4 c^2 x^3 y^4 z^2+134 a^4 b^6 c^2 x^3 y^4 z^2+a^2 b^8 c^2 x^3 y^4 z^2-31 b^10 c^2 x^3 y^4 z^2-142 a^8 c^4 x^3 y^4 z^2+136 a^6 b^2 c^4 x^3 y^4 z^2-48 a^4 b^4 c^4 x^3 y^4 z^2-80 a^2 b^6 c^4 x^3 y^4 z^2+70 b^8 c^4 x^3 y^4 z^2-34 a^6 c^6 x^3 y^4 z^2-138 a^4 b^2 c^6 x^3 y^4 z^2+110 a^2 b^4 c^6 x^3 y^4 z^2-2 b^6 c^6 x^3 y^4 z^2+197 a^4 c^8 x^3 y^4 z^2+40 a^2 b^2 c^8 x^3 y^4 z^2-89 b^4 c^8 x^3 y^4 z^2-79 a^2 c^10 x^3 y^4 z^2+65 b^2 c^10 x^3 y^4 z^2-12 c^12 x^3 y^4 z^2+7 a^12 x^2 y^5 z^2-23 a^10 b^2 x^2 y^5 z^2+22 a^8 b^4 x^2 y^5 z^2+2 a^6 b^6 x^2 y^5 z^2-13 a^4 b^8 x^2 y^5 z^2+5 a^2 b^10 x^2 y^5 z^2+40 a^10 c^2 x^2 y^5 z^2-81 a^8 b^2 c^2 x^2 y^5 z^2+32 a^6 b^4 c^2 x^2 y^5 z^2+14 a^4 b^6 c^2 x^2 y^5 z^2-5 b^10 c^2 x^2 y^5 z^2-149 a^8 c^4 x^2 y^5 z^2+54 a^6 b^2 c^4 x^2 y^5 z^2-14 a^2 b^6 c^4 x^2 y^5 z^2+13 b^8 c^4 x^2 y^5 z^2-54 a^4 b^2 c^6 x^2 y^5 z^2-32 a^2 b^4 c^6 x^2 y^5 z^2-2 b^6 c^6 x^2 y^5 z^2+149 a^4 c^8 x^2 y^5 z^2+81 a^2 b^2 c^8 x^2 y^5 z^2-22 b^4 c^8 x^2 y^5 z^2-40 a^2 c^10 x^2 y^5 z^2+23 b^2 c^10 x^2 y^5 z^2-7 c^12 x^2 y^5 z^2+3 a^12 x y^6 z^2-11 a^10 b^2 x y^6 z^2+14 a^8 b^4 x y^6 z^2-6 a^6 b^6 x y^6 z^2-a^4 b^8 x y^6 z^2+a^2 b^10 x y^6 z^2+a^10 c^2 x y^6 z^2+4 a^8 b^2 c^2 x y^6 z^2-10 a^6 b^4 c^2 x y^6 z^2+4 a^4 b^6 c^2 x y^6 z^2+a^2 b^8 c^2 x y^6 z^2-78 a^8 c^4 x y^6 z^2+42 a^6 b^2 c^4 x y^6 z^2+6 a^4 b^4 c^4 x y^6 z^2-2 a^2 b^6 c^4 x y^6 z^2+38 a^6 c^6 x y^6 z^2-52 a^4 b^2 c^6 x y^6 z^2-10 a^2 b^4 c^6 x y^6 z^2+43 a^4 c^8 x y^6 z^2+17 a^2 b^2 c^8 x y^6 z^2-7 a^2 c^10 x y^6 z^2+4 a^6 b^6 x^6 z^3-12 a^4 b^8 x^6 z^3+12 a^2 b^10 x^6 z^3-4 b^12 x^6 z^3+12 a^4 b^6 c^2 x^6 z^3-24 a^2 b^8 c^2 x^6 z^3+12 b^10 c^2 x^6 z^3+12 a^2 b^6 c^4 x^6 z^3+20 b^8 c^4 x^6 z^3-28 b^6 c^6 x^6 z^3-7 a^10 b^2 x^5 y z^3+9 a^8 b^4 x^5 y z^3+30 a^6 b^6 x^5 y z^3-74 a^4 b^8 x^5 y z^3+57 a^2 b^10 x^5 y z^3-15 b^12 x^5 y z^3-a^8 b^2 c^2 x^5 y z^3-12 a^6 b^4 c^2 x^5 y z^3+6 a^4 b^6 c^2 x^5 y z^3+44 a^2 b^8 c^2 x^5 y z^3-37 b^10 c^2 x^5 y z^3+26 a^6 b^2 c^4 x^5 y z^3+54 a^4 b^4 c^4 x^5 y z^3-118 a^2 b^6 c^4 x^5 y z^3+150 b^8 c^4 x^5 y z^3-2 a^4 b^2 c^6 x^5 y z^3+20 a^2 b^4 c^6 x^5 y z^3-46 b^6 c^6 x^5 y z^3-35 a^2 b^2 c^8 x^5 y z^3-71 b^4 c^8 x^5 y z^3+19 b^2 c^10 x^5 y z^3-a^12 x^4 y^2 z^3-31 a^10 b^2 x^4 y^2 z^3+70 a^8 b^4 x^4 y^2 z^3-2 a^6 b^6 x^4 y^2 z^3-89 a^4 b^8 x^4 y^2 z^3+65 a^2 b^10 x^4 y^2 z^3-12 b^12 x^4 y^2 z^3+8 a^10 c^2 x^4 y^2 z^3+a^8 b^2 c^2 x^4 y^2 z^3-80 a^6 b^4 c^2 x^4 y^2 z^3+110 a^4 b^6 c^2 x^4 y^2 z^3+40 a^2 b^8 c^2 x^4 y^2 z^3-79 b^10 c^2 x^4 y^2 z^3-17 a^8 c^4 x^4 y^2 z^3+134 a^6 b^2 c^4 x^4 y^2 z^3-48 a^4 b^4 c^4 x^4 y^2 z^3-138 a^2 b^6 c^4 x^4 y^2 z^3+197 b^8 c^4 x^4 y^2 z^3+8 a^6 c^6 x^4 y^2 z^3-82 a^4 b^2 c^6 x^4 y^2 z^3+136 a^2 b^4 c^6 x^4 y^2 z^3-34 b^6 c^6 x^4 y^2 z^3+13 a^4 c^8 x^4 y^2 z^3-87 a^2 b^2 c^8 x^4 y^2 z^3-142 b^4 c^8 x^4 y^2 z^3-16 a^2 c^10 x^4 y^2 z^3+65 b^2 c^10 x^4 y^2 z^3+5 c^12 x^4 y^2 z^3-44 a^10 b^2 x^3 y^3 z^3+88 a^8 b^4 x^3 y^3 z^3-88 a^4 b^8 x^3 y^3 z^3+44 a^2 b^10 x^3 y^3 z^3+44 a^10 c^2 x^3 y^3 z^3-124 a^6 b^4 c^2 x^3 y^3 z^3+124 a^4 b^6 c^2 x^3 y^3 z^3-44 b^10 c^2 x^3 y^3 z^3-88 a^8 c^4 x^3 y^3 z^3+124 a^6 b^2 c^4 x^3 y^3 z^3-124 a^2 b^6 c^4 x^3 y^3 z^3+88 b^8 c^4 x^3 y^3 z^3-124 a^4 b^2 c^6 x^3 y^3 z^3+124 a^2 b^4 c^6 x^3 y^3 z^3+88 a^4 c^8 x^3 y^3 z^3-88 b^4 c^8 x^3 y^3 z^3-44 a^2 c^10 x^3 y^3 z^3+44 b^2 c^10 x^3 y^3 z^3+12 a^12 x^2 y^4 z^3-65 a^10 b^2 x^2 y^4 z^3+89 a^8 b^4 x^2 y^4 z^3+2 a^6 b^6 x^2 y^4 z^3-70 a^4 b^8 x^2 y^4 z^3+31 a^2 b^10 x^2 y^4 z^3+b^12 x^2 y^4 z^3+79 a^10 c^2 x^2 y^4 z^3-40 a^8 b^2 c^2 x^2 y^4 z^3-110 a^6 b^4 c^2 x^2 y^4 z^3+80 a^4 b^6 c^2 x^2 y^4 z^3-a^2 b^8 c^2 x^2 y^4 z^3-8 b^10 c^2 x^2 y^4 z^3-197 a^8 c^4 x^2 y^4 z^3+138 a^6 b^2 c^4 x^2 y^4 z^3+48 a^4 b^4 c^4 x^2 y^4 z^3-134 a^2 b^6 c^4 x^2 y^4 z^3+17 b^8 c^4 x^2 y^4 z^3+34 a^6 c^6 x^2 y^4 z^3-136 a^4 b^2 c^6 x^2 y^4 z^3+82 a^2 b^4 c^6 x^2 y^4 z^3-8 b^6 c^6 x^2 y^4 z^3+142 a^4 c^8 x^2 y^4 z^3+87 a^2 b^2 c^8 x^2 y^4 z^3-13 b^4 c^8 x^2 y^4 z^3-65 a^2 c^10 x^2 y^4 z^3+16 b^2 c^10 x^2 y^4 z^3-5 c^12 x^2 y^4 z^3+15 a^12 x y^5 z^3-57 a^10 b^2 x y^5 z^3+74 a^8 b^4 x y^5 z^3-30 a^6 b^6 x y^5 z^3-9 a^4 b^8 x y^5 z^3+7 a^2 b^10 x y^5 z^3+37 a^10 c^2 x y^5 z^3-44 a^8 b^2 c^2 x y^5 z^3-6 a^6 b^4 c^2 x y^5 z^3+12 a^4 b^6 c^2 x y^5 z^3+a^2 b^8 c^2 x y^5 z^3-150 a^8 c^4 x y^5 z^3+118 a^6 b^2 c^4 x y^5 z^3-54 a^4 b^4 c^4 x y^5 z^3-26 a^2 b^6 c^4 x y^5 z^3+46 a^6 c^6 x y^5 z^3-20 a^4 b^2 c^6 x y^5 z^3+2 a^2 b^4 c^6 x y^5 z^3+71 a^4 c^8 x y^5 z^3+35 a^2 b^2 c^8 x y^5 z^3-19 a^2 c^10 x y^5 z^3+4 a^12 y^6 z^3-12 a^10 b^2 y^6 z^3+12 a^8 b^4 y^6 z^3-4 a^6 b^6 y^6 z^3-12 a^10 c^2 y^6 z^3+24 a^8 b^2 c^2 y^6 z^3-12 a^6 b^4 c^2 y^6 z^3-20 a^8 c^4 y^6 z^3-12 a^6 b^2 c^4 y^6 z^3+28 a^6 c^6 y^6 z^3+24 a^6 b^6 x^5 z^4-56 a^4 b^8 x^5 z^4+40 a^2 b^10 x^5 z^4-8 b^12 x^5 z^4+48 a^4 b^6 c^2 x^5 z^4-32 a^2 b^8 c^2 x^5 z^4-16 b^10 c^2 x^5 z^4-24 a^2 b^6 c^4 x^5 z^4+72 b^8 c^4 x^5 z^4-48 b^6 c^6 x^5 z^4-18 a^10 b^2 x^4 y z^4+36 a^8 b^4 x^4 y z^4+48 a^6 b^6 x^4 y z^4-132 a^4 b^8 x^4 y z^4+66 a^2 b^10 x^4 y z^4+18 a^8 b^2 c^2 x^4 y z^4+24 a^6 b^4 c^2 x^4 y z^4+24 a^4 b^6 c^2 x^4 y z^4-66 b^10 c^2 x^4 y z^4+36 a^6 b^2 c^4 x^4 y z^4-24 a^2 b^6 c^4 x^4 y z^4+132 b^8 c^4 x^4 y z^4-36 a^4 b^2 c^6 x^4 y z^4-24 a^2 b^4 c^6 x^4 y z^4-48 b^6 c^6 x^4 y z^4-18 a^2 b^2 c^8 x^4 y z^4-36 b^4 c^8 x^4 y z^4+18 b^2 c^10 x^4 y z^4-5 a^12 x^3 y^2 z^4-65 a^10 b^2 x^3 y^2 z^4+142 a^8 b^4 x^3 y^2 z^4+34 a^6 b^6 x^3 y^2 z^4-197 a^4 b^8 x^3 y^2 z^4+79 a^2 b^10 x^3 y^2 z^4+12 b^12 x^3 y^2 z^4+16 a^10 c^2 x^3 y^2 z^4+87 a^8 b^2 c^2 x^3 y^2 z^4-136 a^6 b^4 c^2 x^3 y^2 z^4+138 a^4 b^6 c^2 x^3 y^2 z^4-40 a^2 b^8 c^2 x^3 y^2 z^4-65 b^10 c^2 x^3 y^2 z^4-13 a^8 c^4 x^3 y^2 z^4+82 a^6 b^2 c^4 x^3 y^2 z^4+48 a^4 b^4 c^4 x^3 y^2 z^4-110 a^2 b^6 c^4 x^3 y^2 z^4+89 b^8 c^4 x^3 y^2 z^4-8 a^6 c^6 x^3 y^2 z^4-134 a^4 b^2 c^6 x^3 y^2 z^4+80 a^2 b^4 c^6 x^3 y^2 z^4+2 b^6 c^6 x^3 y^2 z^4+17 a^4 c^8 x^3 y^2 z^4-a^2 b^2 c^8 x^3 y^2 z^4-70 b^4 c^8 x^3 y^2 z^4-8 a^2 c^10 x^3 y^2 z^4+31 b^2 c^10 x^3 y^2 z^4+c^12 x^3 y^2 z^4-12 a^12 x^2 y^3 z^4-79 a^10 b^2 x^2 y^3 z^4+197 a^8 b^4 x^2 y^3 z^4-34 a^6 b^6 x^2 y^3 z^4-142 a^4 b^8 x^2 y^3 z^4+65 a^2 b^10 x^2 y^3 z^4+5 b^12 x^2 y^3 z^4+65 a^10 c^2 x^2 y^3 z^4+40 a^8 b^2 c^2 x^2 y^3 z^4-138 a^6 b^4 c^2 x^2 y^3 z^4+136 a^4 b^6 c^2 x^2 y^3 z^4-87 a^2 b^8 c^2 x^2 y^3 z^4-16 b^10 c^2 x^2 y^3 z^4-89 a^8 c^4 x^2 y^3 z^4+110 a^6 b^2 c^4 x^2 y^3 z^4-48 a^4 b^4 c^4 x^2 y^3 z^4-82 a^2 b^6 c^4 x^2 y^3 z^4+13 b^8 c^4 x^2 y^3 z^4-2 a^6 c^6 x^2 y^3 z^4-80 a^4 b^2 c^6 x^2 y^3 z^4+134 a^2 b^4 c^6 x^2 y^3 z^4+8 b^6 c^6 x^2 y^3 z^4+70 a^4 c^8 x^2 y^3 z^4+a^2 b^2 c^8 x^2 y^3 z^4-17 b^4 c^8 x^2 y^3 z^4-31 a^2 c^10 x^2 y^3 z^4+8 b^2 c^10 x^2 y^3 z^4-c^12 x^2 y^3 z^4-66 a^10 b^2 x y^4 z^4+132 a^8 b^4 x y^4 z^4-48 a^6 b^6 x y^4 z^4-36 a^4 b^8 x y^4 z^4+18 a^2 b^10 x y^4 z^4+66 a^10 c^2 x y^4 z^4-24 a^6 b^4 c^2 x y^4 z^4-24 a^4 b^6 c^2 x y^4 z^4-18 a^2 b^8 c^2 x y^4 z^4-132 a^8 c^4 x y^4 z^4+24 a^6 b^2 c^4 x y^4 z^4-36 a^2 b^6 c^4 x y^4 z^4+48 a^6 c^6 x y^4 z^4+24 a^4 b^2 c^6 x y^4 z^4+36 a^2 b^4 c^6 x y^4 z^4+36 a^4 c^8 x y^4 z^4+18 a^2 b^2 c^8 x y^4 z^4-18 a^2 c^10 x y^4 z^4+8 a^12 y^5 z^4-40 a^10 b^2 y^5 z^4+56 a^8 b^4 y^5 z^4-24 a^6 b^6 y^5 z^4+16 a^10 c^2 y^5 z^4+32 a^8 b^2 c^2 y^5 z^4-48 a^6 b^4 c^2 y^5 z^4-72 a^8 c^4 y^5 z^4+24 a^6 b^2 c^4 y^5 z^4+48 a^6 c^6 y^5 z^4+48 a^6 b^6 x^4 z^5-72 a^4 b^8 x^4 z^5+16 a^2 b^10 x^4 z^5+8 b^12 x^4 z^5+24 a^4 b^6 c^2 x^4 z^5+32 a^2 b^8 c^2 x^4 z^5-40 b^10 c^2 x^4 z^5-48 a^2 b^6 c^4 x^4 z^5+56 b^8 c^4 x^4 z^5-24 b^6 c^6 x^4 z^5-19 a^10 b^2 x^3 y z^5+71 a^8 b^4 x^3 y z^5+46 a^6 b^6 x^3 y z^5-150 a^4 b^8 x^3 y z^5+37 a^2 b^10 x^3 y z^5+15 b^12 x^3 y z^5+35 a^8 b^2 c^2 x^3 y z^5-20 a^6 b^4 c^2 x^3 y z^5+118 a^4 b^6 c^2 x^3 y z^5-44 a^2 b^8 c^2 x^3 y z^5-57 b^10 c^2 x^3 y z^5+2 a^6 b^2 c^4 x^3 y z^5-54 a^4 b^4 c^4 x^3 y z^5-6 a^2 b^6 c^4 x^3 y z^5+74 b^8 c^4 x^3 y z^5-26 a^4 b^2 c^6 x^3 y z^5+12 a^2 b^4 c^6 x^3 y z^5-30 b^6 c^6 x^3 y z^5+a^2 b^2 c^8 x^3 y z^5-9 b^4 c^8 x^3 y z^5+7 b^2 c^10 x^3 y z^5-7 a^12 x^2 y^2 z^5-40 a^10 b^2 x^2 y^2 z^5+149 a^8 b^4 x^2 y^2 z^5-149 a^4 b^8 x^2 y^2 z^5+40 a^2 b^10 x^2 y^2 z^5+7 b^12 x^2 y^2 z^5+23 a^10 c^2 x^2 y^2 z^5+81 a^8 b^2 c^2 x^2 y^2 z^5-54 a^6 b^4 c^2 x^2 y^2 z^5+54 a^4 b^6 c^2 x^2 y^2 z^5-81 a^2 b^8 c^2 x^2 y^2 z^5-23 b^10 c^2 x^2 y^2 z^5-22 a^8 c^4 x^2 y^2 z^5-32 a^6 b^2 c^4 x^2 y^2 z^5+32 a^2 b^6 c^4 x^2 y^2 z^5+22 b^8 c^4 x^2 y^2 z^5-2 a^6 c^6 x^2 y^2 z^5-14 a^4 b^2 c^6 x^2 y^2 z^5+14 a^2 b^4 c^6 x^2 y^2 z^5+2 b^6 c^6 x^2 y^2 z^5+13 a^4 c^8 x^2 y^2 z^5-13 b^4 c^8 x^2 y^2 z^5-5 a^2 c^10 x^2 y^2 z^5+5 b^2 c^10 x^2 y^2 z^5-15 a^12 x y^3 z^5-37 a^10 b^2 x y^3 z^5+150 a^8 b^4 x y^3 z^5-46 a^6 b^6 x y^3 z^5-71 a^4 b^8 x y^3 z^5+19 a^2 b^10 x y^3 z^5+57 a^10 c^2 x y^3 z^5+44 a^8 b^2 c^2 x y^3 z^5-118 a^6 b^4 c^2 x y^3 z^5+20 a^4 b^6 c^2 x y^3 z^5-35 a^2 b^8 c^2 x y^3 z^5-74 a^8 c^4 x y^3 z^5+6 a^6 b^2 c^4 x y^3 z^5+54 a^4 b^4 c^4 x y^3 z^5-2 a^2 b^6 c^4 x y^3 z^5+30 a^6 c^6 x y^3 z^5-12 a^4 b^2 c^6 x y^3 z^5+26 a^2 b^4 c^6 x y^3 z^5+9 a^4 c^8 x y^3 z^5-a^2 b^2 c^8 x y^3 z^5-7 a^2 c^10 x y^3 z^5-8 a^12 y^4 z^5-16 a^10 b^2 y^4 z^5+72 a^8 b^4 y^4 z^5-48 a^6 b^6 y^4 z^5+40 a^10 c^2 y^4 z^5-32 a^8 b^2 c^2 y^4 z^5-24 a^6 b^4 c^2 y^4 z^5-56 a^8 c^4 y^4 z^5+48 a^6 b^2 c^4 y^4 z^5+24 a^6 c^6 y^4 z^5+28 a^6 b^6 x^3 z^6-20 a^4 b^8 x^3 z^6-12 a^2 b^10 x^3 z^6+4 b^12 x^3 z^6-12 a^4 b^6 c^2 x^3 z^6+24 a^2 b^8 c^2 x^3 z^6-12 b^10 c^2 x^3 z^6-12 a^2 b^6 c^4 x^3 z^6+12 b^8 c^4 x^3 z^6-4 b^6 c^6 x^3 z^6-7 a^10 b^2 x^2 y z^6+43 a^8 b^4 x^2 y z^6+38 a^6 b^6 x^2 y z^6-78 a^4 b^8 x^2 y z^6+a^2 b^10 x^2 y z^6+3 b^12 x^2 y z^6+17 a^8 b^2 c^2 x^2 y z^6-52 a^6 b^4 c^2 x^2 y z^6+42 a^4 b^6 c^2 x^2 y z^6+4 a^2 b^8 c^2 x^2 y z^6-11 b^10 c^2 x^2 y z^6-10 a^6 b^2 c^4 x^2 y z^6+6 a^4 b^4 c^4 x^2 y z^6-10 a^2 b^6 c^4 x^2 y z^6+14 b^8 c^4 x^2 y z^6-2 a^4 b^2 c^6 x^2 y z^6+4 a^2 b^4 c^6 x^2 y z^6-6 b^6 c^6 x^2 y z^6+a^2 b^2 c^8 x^2 y z^6-b^4 c^8 x^2 y z^6+b^2 c^10 x^2 y z^6-3 a^12 x y^2 z^6-a^10 b^2 x y^2 z^6+78 a^8 b^4 x y^2 z^6-38 a^6 b^6 x y^2 z^6-43 a^4 b^8 x y^2 z^6+7 a^2 b^10 x y^2 z^6+11 a^10 c^2 x y^2 z^6-4 a^8 b^2 c^2 x y^2 z^6-42 a^6 b^4 c^2 x y^2 z^6+52 a^4 b^6 c^2 x y^2 z^6-17 a^2 b^8 c^2 x y^2 z^6-14 a^8 c^4 x y^2 z^6+10 a^6 b^2 c^4 x y^2 z^6-6 a^4 b^4 c^4 x y^2 z^6+10 a^2 b^6 c^4 x y^2 z^6+6 a^6 c^6 x y^2 z^6-4 a^4 b^2 c^6 x y^2 z^6+2 a^2 b^4 c^6 x y^2 z^6+a^4 c^8 x y^2 z^6-a^2 b^2 c^8 x y^2 z^6-a^2 c^10 x y^2 z^6-4 a^12 y^3 z^6+12 a^10 b^2 y^3 z^6+20 a^8 b^4 y^3 z^6-28 a^6 b^6 y^3 z^6+12 a^10 c^2 y^3 z^6-24 a^8 b^2 c^2 y^3 z^6+12 a^6 b^4 c^2 y^3 z^6-12 a^8 c^4 y^3 z^6+12 a^6 b^2 c^4 y^3 z^6+4 a^6 c^6 y^3 z^6 = 0