Not just tetrahedra. In this case, I used triangular prisms.
Also, this UV lock testing was for the purpose of what I'm about to write:
You basically have a 'grid' of triangles in the top view, which are actually either tetrahedra or triangular prisms.
However, you want a seamless texture, but it has to be applied on a huge surface yet stay detailed enough:
(this one is small, so 512x512 is enough)
You'd have to have four 1024x256 textures applied on 4 rows.
This testing was simply my way to check if the grid should be "strict":
Or if it can also be a "free" grid:
Here's why:
The free grid would have seams.
But, this way, we can avoid seams!