Barth Sextic
The Barth-sextic is a Sextic Surface in complex three-dimensional projective space having the maximum possible number ofOrdinary Double Points (65). It is given by the implicit equation
where
is the Golden Mean, and 
is a parameter (Endraß, Nordstrand), taken as 
in the above plot.The Barth sextic is invariant under the Icosahedral Group. Under the map
the surface is the eightfold cover of the Cayley Cubic (Endraß).See also Algebraic Surface, Barth Decic, Cayley Cubic, Ordinary Double Point, Sextic Surface
References
Barth, W. ``Two Projective Surfaces with Many Nodes Admitting the Symmetries of the Icosahedron.'' J. Alg. Geom. 5, 173-186, 1996. Endraß, S. ``Flächen mit vielen Doppelpunkten.'' DMV-Mitteilungen 4, 17-20, 4/1995. Endraß, S. ``Barth's Sextic.''http://www.mathematik.uni-mainz.de/AlgebraischeGeometrie/docs/Ebarthsextic.shtml. Nordstrand, T. ``Barth Sextic.'' http://www.uib.no/people/nfytn/sexttxt.htm.
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