The fractal surface of a strange attractor

The following sextic was found by W. Barth. It has 65 ordinary double points, the maximal possible number.

Surface with constant Gaussian curvature

This surface by Xah Lee, which he calls the Borg Cube, is given by the equation
sin(xy) + sin(yz) + sin(zx) = 0

By Daniel Piker

Clebsch Diagonal Cubic

The surface is given by the equation x^3 + y^3 + z^3 + w^3 + t^3 = 0, restricted to the values x, y, z, w, t, such that x + y + z + w + t = 0.

These beautiful origami pieces were constructed by mathematicians Erik and Martin Demaine (first image) and Thomas Hull (second image) to investigate the surfaces that result from different kinds of pleated folding.