Octahedral Symmetry on a Sphere

Here is openSCAD code which covers a sphere with a pattern that displays octahedral symmetry.

Any planar pattern with a three or four fold rotation axis at right angles to the origin can be used. Copies of the pattern are "bent" and subtracted from the surface of the sphere.

To illustrate the method groups of Sierpinski triangles arranged to have three and four fold rotation axes were used. The files are sierpinski_triangles_3.dxf and sierpinski_triangles_4.dxf. See the images at the l