Inspired by Angus once again, I decided to have a look at how I would design a tetrahedron in OpenSCAD.
https://youtu.be/5YwvK0dcfmw

It turns out the maths are quite simple. I found everything I needed on Wikipedia.
https://en.wikipedia.org/wiki/Equilateral_triangle

I made a simple module to take care of the task, so I decided to share it.