Tetrahedral Symmetry on a Sphere

thingiverse

Here is openSCAD code which covers a sphere with a pattern displaying tetrahedral symmetry. The code uses the same technique as that described in things 39424 and 39818 and completes the method based on the Platonic solids. A tetrahedron has 4 three fold rotation axis which pass through the vertices. The vertices are mapped to a sphere and the 3 fold patterns centered at the mapped vertices. The pattern used was sierpinski_triangles_3.dxf; the dxf file and a picture are available at thing:39424. Stl files are: sierpinski_tetrahedral_small.stl a sphere 50 mm in diameter sierpinski_tetrahedral_large.stl a truncated sphere 70 mm in diameter. One interesting thing is that a three fold pattern generated from the Sierpinski triangles by tetrahedral symmetry resembles a four fold pattern generated by octahedral symmetry (thing:39424) and a five fold pattern generated by icosahedral symmetry (thing:39977). See the image at the lower left. The openSCAD code that generated the spheres is gen_tetrahedral_symmetry.scad. Instructions The small stl files is a sphere and needs to be printed with external support. I used 3 shells and 5% infill on my Replicator and it printed in about 2 hours. The large stl file is a truncated sphere. It can be printed directly on the build platform and takes three hours.