Geodesic
From Permutation Points to Permutation Cubics
Journal for geometry and graphics, Tome 26 (2022) no. 2, pp. 253-269.

Voir la notice de l'article provenant de la source Heldermann Verlag

The trilinear coordinates of a point V in the plane of a triangle can be permuted in six ways which yields the six permutation points of V. These six points always lie on a single conic, called the permutation conic. A natural variant or generalization seems to be: The six permutation points of V together with the six permutation points of V's image under a certain quadratic Cremona transformation γ comprise a set of twelve points that always lie on a single cubic which we shall call the permutation cubic of V with respect to γ. In the present paper we shall discuss especially the cases where γ is the isogonal or the isotomic conjugation. Properties and remarkable features of these cubics shall be elaborated.
Classification : 14H45, 51N35
Mots-clés : Permutation point, triangle cubic, permutation cubic, triangle center, antiorthic axis, Mandart circumellipse 
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     author = {B. Odehnal },
     title = {From {Permutation} {Points} to {Permutation} {Cubics}},
     journal = {Journal for geometry and graphics},
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     number = {2},
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B. Odehnal . From Permutation Points to Permutation Cubics. Journal for geometry and graphics, Tome 26 (2022) no. 2, pp. 253-269. http://geodesic.mathdoc.fr/item/JGG_2022_26_2_JGG_2022_26_2_a4/