Solid of constant width in OpenSCAD

Here’s a basic OpenSCAD script generating a model of a solid of constant width based on a tetrahedron. Now to figure out how to position it with constant distance to the plane…

u = 10;
diameter = sqrt(8*u*u);
intersection() {
  translate([u,u,u]) sphere(diameter);
  translate([u,-u,-u]) sphere(diameter);
  translate([-u,u,-u]) sphere(diameter);
  translate([-u,-u,u]) sphere(diameter);
}

Solid of constant width

Or check out this Numberphile video: