Model originally uploaded to Thingiverse at https://www.thingiverse.com/thing:3620748.
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.