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∑ a (b - c) x (y^2 + z^2) = 0

X(2), X(239), X(335), X(536), X(3227), X(11611), X(19623), X(29908), X(40844), X(40862), X(40874), X(40881), X(44330), X(46795), X(46796), X(46797), X(46798), X(46799), X(46800), X(46801), X(46802), X(46803), X(46804), X(46805), X(52517)

infinite points of the Steiner ellipse

Geometric properties :

See K1303 for properties and a generalization. K1305 is a member of CL031.

The isogonal transform of K1305 is cK0(#X6, X667). Its barycentric product by X(1) is cK(#X1, X649).

K1305 is the G-Hirst transform of the circum-conic with perspector X(513) passing through X(i) for i = 1, 2, 28, 57, 81, 88, 89, 105, 274, 277, 278, 279, 291, 330, 367, 955, 957, 959, 961, 985, 1002, 1022, 1123, 1170, 1219, 1224, 1255, 1257, 1258, 1280, 1336, 1390, 1422, 1432, 1929, 2006, 2224, 2282, 2306, 2362, 2401, 2982, 2990, 3227, etc.

Let (L1), (L2) be two parallels to the line {2, 37, 75, ...} and symmetric in G. Let (C1), (C2) be their respective isotomic transforms. (L1), (C2) meet at M1, N1 and (L2), (C1) meet at M2, N2. These four points lie on K1305.