As soon as it was decited we need a LED matrix, I started to design that thing on my CAD program. I use VariCAD, because some years ago this was the only affordable 3D program running on linux machines. So knew I would have a nice lasercutter at hand in our local fablab/open garage thingy (Die Werke). This way you can easily use rectangle shapes to make system, where the parts nice link together (holes for the LEDs missing):

The size of the cubic was tested with one of the LEDs some white cardboard aon a breadboard.

After designing that for the whole thing, it had to be cut into pieces that would fit into the lasercutter and still interlink nicely for stability reasons:

red markings show the link sction, black one how it's "captured" by the horizontal parts. Backplane is splitted in 5 parts, which interscet also. I made several links with different parts in lenght, so I could spread this weak points evenly in the construction. Here is the whole picture:

horizontal parts needed noe splitting

vertical parts: The way I designed them, there are two parts, depending whech end they end up (because the design of my splitting line dosen't allow flipping). So I made them even (blue) and uneven (green) to end up with one type on each end of the row. The backplanes have cutting lines which prevent them crossing the complete hight/width.

I will upload all CAD data (dxf parts already sorted for cutting on a 300x600mm bed and the uncutted parts as well as the 3D step data)