In mathematics, Wiman's sextic is a degree 6 plane curve with four

nodes In general, a node is a localized swelling (a "knot") or a point of intersection (a Vertex (graph theory), vertex). Node may refer to: In mathematics *Vertex (graph theory), a vertex in a mathematical graph *Vertex (geometry), a point where two ...

studied by . It is given by the equation (in

homogeneous coordinates In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work , are a system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry. T ...

) :

x^6+y^6+z^6 + (x^2+y^2+z^2)(x^4+y^4+z^4)=12 x^2y^2z^2

Its

normalization Normalization or normalisation refers to a process that makes something more normal or regular. Most commonly it refers to: * Normalization (sociology) or social normalization, the process through which ideas and behaviors that may fall outside of ...

is a

genus Genus ( plural genera ) is a taxonomic rank used in the biological classification of extant taxon, living and fossil organisms as well as Virus classification#ICTV classification, viruses. In the hierarchy of biological classification, genus com ...

6 curve with automorphism group isomorphic to the symmetric group ''S''₅.

References

* *{{Citation , last1=Wiman , first1=A., authorlink=Anders Wiman , title=Zur Theorie der endlichen Gruppen von birationalen Transformationen in der Ebene , year=1896 , journal=

Mathematische Annalen ''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, ...

, volume=48 , issue=1–2, pages=195–240 , doi=10.1007/BF01446342, s2cid=123516972, url=https://zenodo.org/record/2001310 Sextic curves