Reuleaux tetrahedron - Solid of "almost" constant width (OpenSCAD)

After watching Angus video, I got curious and decided to experiment with the concept of "solid of constant width". https://youtu.be/2eUWT9cI23o

I implemented it based on a tetrahedron.

[Update 06/05/2017]: It turns out that this shape is called a Reuleaux tetrahedron, and it's NOT a shape of constant width. It has a slight extra width between 2 opposite edges. The popular solution to make it constant width is to implement the Meissner tetrahedra. The mathematician in me doesn't like that none-symmetrical shape. It looks like a patched shape. I'm pretty sure we can apply "half" the correction to all 6 edges to make a symmetrical shape. I will have to do more studies on the subject and understand the math before trying to implement it.

According to this paper, the shape I'm trying to implement is called a Spheroform tetrahedron: http://www.xtalgrafix.com/Reuleaux/Spheroform%20Tetrahedron.pdf

I found an OpenSCAD implementation on Thingiverse: http://www.thingiverse.com/thing:408157

[Edit 2018-08-16] Angus made a 3D model of this shape with Fusion 360, and it is a lot easier to print. You can download his model for free. Have a look at his video (download link in video description): https://youtu.be/8wPu2Y4hk6A

Category: Math Art