Tetrahedral Symmetry on a Sphere

thingiverse

This openSCAD code creates a sphere with a pattern exhibiting tetrahedral symmetry, similar to things 39424 and 39818. The technique draws from Platonic solids' principles. Tetrahedrons possess four three-fold rotation axes through their vertices; these are mapped onto the sphere while centering 3-fold patterns at the corresponding vertices. The Sierpinski triangles' pattern (sierpinski_triangles_3.dxf) is utilized in this design, with related dxf file and image accessible via thing:39424. The output includes two STL files - sierpinski_tetrahedral_small.stl for a 50mm diameter sphere and sierpinski_tetrahedral_large.stl for a 70mm truncated sphere. Interestingly, the three-fold pattern generated by tetrahedral symmetry from Sierpinski triangles resembles a four-fold pattern formed by octahedral symmetry (thing:39424) and a five-fold pattern created by icosahedral symmetry (thing:39977). The openSCAD code responsible for generating these spheres is gen_tetrahedral_symmetry.scad. The small STL file, sierpinski_tetrahedral_small.stl, requires external support and can be printed in about 2 hours with 3 shells and 5% infill on a Replicator. The large STL file, sierpinski_tetrahedral_large.stl, is a truncated sphere printable directly onto the build platform, taking around three hours for completion.