Symmetric Spheroform Tetrahedron

cults3d

Spheroform with Tetrahedral Symmetry Inspired by Angus one Friday night Ultimate Solids of Constant Width. I thought I would combine the ideas of tetrahedral symmetry and a low poly/fast OpenSCAD implementation. Based on Solids of constant width – the Meissner Tetrahedron – in OpenSCAD ceptimus Modified for tetrahedral symmetry using calculations from xtalgrafix With a few more optimisations of my own. Fast enough now to crank up the resolution and generate multiple variants as parts. UPDATE: Initial approximations using linear_extruded circles or the rotate_extrude ceptimus code introduced errors which would probably be measurable. I updated the scad to use spheres (well, polygons) which blew out the compile time. Then further optimised for symmetry to bring it back down again. UPDATE2: Now calculating envelope surface directly and using polyhedron. UPDATE3: We're just a few spheres away from implementing the whole thing in a single polyhedron avoiding any expensive intersection, union or hull operations altogether. We can also tailor our sphere mesh to remove any unsightly seams or internal faces.Single Polyhedron Symmetric Spheroform Tetrahedron.