Togliatti surface

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The surface with w=1 (real points, bounded by a sphere with radius=6).

In algebraic geometry, a Togliatti surface is a nodal surface of degree five with 31 nodes. The first examples were constructed by Eugenio G. Togliatti (1940). Beauville (1980) proved that 31 is the maximum possible number of nodes for a surface of this degree, showing this example to be optimal.

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