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 upper bound is 174. The equations of the surfaces are




where w is a parameter taken as w = 1 in the above plots. All ordinary double points of are real, while 24 of those in are complex. The surfaces were discovered in a five-dimensional family of octics with 112 nodes, and are invariant under the group.