“The Barth-sextic is a sextic surface in complex three-dimensional projective space having the maximum possible number of ordinary double points, namely 65. The surface was discovered by Wolf Barth in 1994, and is given by the implicit equation:

where phi is the golden ratio.” ~ MathWorld. We can write short Wolfram Language code ( by Jeff Bryant ) and export to .STL format to interact in 3D via Sketchfab:

ContourPlot3D[
4*(phi^2*x^2 - y^2)*
(phi^2*y^2 - z^2)*
(phi^2*z^2 - x^2) - 
(1 + 2*phi)*
(x^2 + y^2 + z^2 - w^2)^2 * w^2 ,
 {x, -5, 5}, {y, -5, 5}, {z, -5, 5}, 
Contours -> {0}, PlotPoints -> 75,
ContourStyle -> Specularity[White, 50], 
Mesh -> None,MaxRecursion -> 2,
RegionFunction -> 
(Sqrt[#1^2 + #2^2 + #3^2] <= 5 &),
ImageSize -> 600, Boxed -> False, 
Axes -> False, Background -> Black,
 SphericalRegion -> True, 
ViewPoint -> {0.38, -3.33, 0.49},
Lighting -> {
{"Directional", RGBColor[0.5, 0.5, 1],
   ImageScaled[{0, 1, 0}]},
{"Directional", RGBColor[1, 0.5, 0.5],
   ImageScaled[{1, -1, 0}]}, 
{"Directional", RGBColor[0.5, 1, 0.5],
   ImageScaled[{-1, -1, 0}]}}]

More information and images at AMS blogs where you can find the disection image above or at Wolfram|Alpha engine: