Rounded symmetric spheroform tetrahedron

thingiverse

This is a rounded version of [Patrick Roberts' spheroform with tetrahedral symmetry](http://www.xtalgrafix.com/Spheroform.htm) that retains the constant-width spheroform property. This is a remix using tmackay's variable-detail polyhedral OpenSCAD design combined with Jamie_K's geodesic sphere design. Here's how it works: For a given width and corner radius *r*, shrink the spheroform tetrahedron to width−2*r*, and then perform a Minkowski sum of the shrunken part with a sphere of radius *r*. This offsets the surface back out to the original width, but the sharp corners become rounded (the corner of the original tetrahedron becomes the center of the spherical corner). At the extremes, when *r*=0 then the width is just the original width, but as width−2*r* approaches zero, the Minkowski-sum shape approaches a sphere. Everything in between also has constant width. The STL file included is a 40 mm tetrahedral spheroform with 6 mm radius corners.