Sylvester’s amphigenous surface
In the 19th century Sylvester described a surface for studying the number of real roots of a polynomial. Henrici later constructed a model of this. This is a modern version.
The Henrici cubic with three cusps
In the 19th century, Olaus Henrici constructed a model of a quite symmetric cubic surface. This is a modern variant of it, allowing also to look "inside" of it from the bottom.