Solitude, a singular algebraic surface of degree four. This is the set of real points for which ```x^2yz +xy^2+y^3+y^3z-x^2*z^2 = 0.```

Has two holes, and two singular lines, one of which exists nakedly in the voids in the surface!

Provided are three files:

• `solitude_thickened.stl` -- has the normal vectors fixed, and is thickened for printing.
• `solitude_raw.stl` -- raw triangulation coming from Bertini_real. Since the program works in arbitrary dimensions, I make no effort to control normals from it -- they don't exist for 4- and higher-dimensional surfaces, but instead a tangent space which is not immediately useful for 3d printing. Hence, the surface was thickened in Blender, before being passed through Microsoft's 3D Builder to fix internal geometry. This version is not directly suitable for 3d printing.
• `input` -- the Bertini_real input file used to compute it.

Computed with a Numerical Algebraic Geometry program I wrote, called Bertini_real and printed as part of my long-term project to reproduce Herwig Hauser's gallery of algebraic surface ray-traces in my own gallery of 3d prints. The ACM ToMS algorithm number is 976; the major published paper is DOI 10.1145/3056528 with several others preceding. Bertini_real implements the implicit function theorem for algebraic surfaces and curves in any (reasonable) number of variables.

See also, my Thingiverse collection of algebraic surfaces.