Tetrahedron Gantry Concept

This is just an idea. I don't know how feasible it is, or whether it's worth building or calibrating. In fact, I don't know almost anything about it...

It's a somewhat different 3D gantry design based around a tetrahedron. There are three axes, belt-driven or what-have-you, and each is connected by a sarrus linkage to the end platform.

I like it because it's extremely stable (tetrahedron) and every axis is exactly the same.

However, (1) it needs complex maths, (2) there's a large footprint, and (3) nobody's actually tried it.

Any thoughts?