Endraß Octic
Endraß surfaces are a pair of Octic Surfaces which have 168 Ordinary Double Points. This is the maximum number known to exist for an Octic Surface, although the rigorous upperbound is 174. The equations of the surfaces 
are
 | |
 | |
 |
is a parameter taken as 
in the above plots. All Ordinary Double Points of 
are real, while 24 of those in 
are complex. The surfaces were discovered in a 5-Dfamily of octics with 112 nodes, and are invariant under the Group 
.See also Octic Surface
References
Endraß, S. ``Octics with 168 Nodes.''http://www.mathematik.uni-mainz.de/AlgebraischeGeometrie/docs/Eendrassoctic.shtml. Endraß, S. ``Flächen mit vielen Doppelpunkten.'' DMV-Mitteilungen 4, 17-20, 4/1995. Endraß, S. ``A Proctive Surface of Degree Eight with 168 Nodes.'' J. Algebraic Geom. 6, 325-334, 1997.
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