Geodesic
Symmetric sextics and auxiliary conics
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 6, Tome 279 (2001), pp. 154-167

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Rigid isotopy classes of nonsingular curves of degree 6 in $\mathbb RP^2$ are considered. The previously-known list of all the classes containing symmetric curves is obtained by elementary means. The proof of the fact that a curve in a given rigid isotopy class cannot be symmetric involves studing the position of such a curve with respect to auxuliary conics. 
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     author = {V. S. Itenberg and I. V. Itenberg},
     title = {Symmetric sextics and auxiliary conics},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {154--167},
     publisher = {mathdoc},
     volume = {279},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_279_a8/}
}
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V. S. Itenberg; I. V. Itenberg. Symmetric sextics and auxiliary conics. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 6, Tome 279 (2001), pp. 154-167. http://geodesic.mathdoc.fr/item/ZNSL_2001_279_a8/