Back to the drawing board                                         

I have put my analytical hat on in order to methodically approach the Mystery of Non Fitting Triangles.
The first problem: due to its shape (tapering angles) I can't accurately measure the size of the triangle.
Solution: make slightly oversized model and see how my shapes fit on top.
 If I haven't totally blundered in making the shapes, the angles should match....

and they do.
So do the angles on the brackets.
in the moment of practical inspiration I drew the clay shape on the transparency and copied it 6 times. Position of the holes is important.
And there I found it!
The hole on the bracket needs to be 5 mm further from the center. Therefore the bracket needs to be 5 mm longer on each side, as you can see on the paper model (right).

So, back to the bracket making, measuring, connecting and testing the theory....
and this time it works:

Do you want to see it right way up?

It fits! It fits! It fits!

(Of course, that is only first 6 out of 180. And I made 12 brackets out of 540....)

But I will keep those thoughts at bay, and finish with a quote from the father of geodesic domes:

“When I am working on a problem, I never think about beauty........ but 

when I have finished, if the solution is not beautiful, I know it is wrong.” 

―Richard Buckminster Fuller