A quintic surface is an algebraic surface of degree 5. Togliatti (1940, 1949) showed that quintic surfaces having 31 ordinary
double points exist, although he did not explicitly derive equations for such
surfaces. Beauville (1978) subsequently proved that 31 double points was the maximum
possible, and quintic surfaces having 31 ordinary
double points are therefore sometimes called Togliatti
surfaces. van Straten (1993) subsequently constructed a three-dimensional family
of solutions and in 1994, Barth derived the example known as the dervish.

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E. G. "Una notevole superficie del ordine con soli punti doppi isolati." Vierteljschr.
Naturforsch. Ges. Zürich85, 127-132, 1940.Togliatti,
E. "Sulle superfici monoidi col massimo numero di punti doppi." Ann.
Mat. Pura Appl.30, 201-209, 1949.van Straten, D. "A
Quintic Hypersurface in
with 130 Nodes." Topology32, 857-864, 1993.