Symmetric Spheroform Tetrahedron

thingiverse

Spheroform with Tetrahedral Symmetry Inspired by Angus one Friday night [Ultimate Solids of Constant Width](https://www.youtube.com/watch?v=fOojOfpcPZM), I thought it would be a great idea to combine the concepts of tetrahedral symmetry and a low poly/fast OpenSCAD implementation. Based on Solids of constant width – the Meissner Tetrahedron – in OpenSCAD [ceptimus](http://ceptimus.co.uk/?p=345), I modified it for tetrahedral symmetry using calculations from [xtalgrafix](http://www.xtalgrafix.com/Spheroform2.htm). With a few more optimizations of my own, the code is now fast enough 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 optimized 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](https://www.thingiverse.com/thing:3636287).