Revolute joints for tetrahedral spaceframe

[Anonymous]

Hi all, 

I'm working on generating build instructions for a spaceframe made of equal-length members bent at 70 and 110 degrees:

As you can see, as-built assembly involves a sort overlap weave of the tabs, which have a small amount of flexibility inherent to steel sheets required to properly assemble:

 

As you might predict, when I try to set up this exact assembly with 3x 70-bent members (to form the vertex of a tetrahedron), the joints don't quite align:

So, I'm fudging the assembly a bit by mating the parts to overlap each other, which seems to have done the trick as far as hole alignment goes - however, my problem is that when I set all the joints to revolve, the assembly inverts itself:

 Any ideas on how to get this assembly done properly?

70 degree member attached for reference.

Thanks,

Charlie

[Anonymous]

I've managed to get the first vertex set up but now I can't get any of the edges to line up. This seems to be the challenging part:

[Anonymous]

Here's the essence of the problem:

Why is this happening?

[Anonymous · Accepted solution]

I realized that this problem is occurring because the dihedral angle is not exactly 70 degrees, it is calculated by arccos(1/3) which is approx 70.5288.