Frame
TODO: This is only a rough draft and really only contains the beginnings of a proper page about this subject
The frame is a simple box
By using 2020 extrusion and enclosing the sides, top and bottom the BBox resembles a tall box.
While a basic box made from 2020 extrusion would use 12 pieces (4 for the top square, 4 for the bottom square and 4 vertical uprights joining the top and bottom squares) the BBox uses 3 additional pieces of extrusion for a middle section. So in total the BBox uses 11 horizontal pieces and 4 vertical pieces. The exact dimensiions of these pieces is described in the section of this document titled The sizes of things
Keeping everything square
It is important to ensure that horizontal and vertical members are perpendicular to each other (90 degrees). This is what it means to be "square". If your horizontal extrusions are cut to the same exact dimensions, they can actually be a little bit off (say 301mm instead of a desired 300mm) and everything will still work fine as long as they are all the same length.
This is why I suggest you assemble the frame on a flat and level surface. A glass or stone countertop is ideal for this.
TODO: Show pic here
Okay...now I'm going to mess with your mind. The frame doesn't actually have to be perfectly square all the way around. While you should strive for that level of perfection (as it will make everything much easier), it would be more accurate to say that certain parts of the frame must be parallel to one another.
For example, the left and right middle horizonal members that the Y-rods lie above must be parallel to one another as well as be in the same plane, but the left and right horizoontal members on the top and bottom squares can be off from this ideal by a little bit. By ensuring the middle left and right horizontal members are parallel we can be assured the gantry will slide smoothly along Y without any binding.
TODO: Show pic here
Joining the extrusion pieces
I would expect that using blind joints would be the optimal method of joining the pieces. You would need to ensure that the ends of your pieces were cut perfectly square which one would hope be the case when buying pre-cut extrusion. However I have yet to build a BBox using this method as I did not have good luck cutting my ends perfectly square.
So instead I've used 3-way corner connectors. I have found that these are a little more forgiving and can help you achieve squareness even if your extrusion ends are not precisely cut square.
Lastly it should be possible to use triangular corner connectors at the inner corners of where extrusions meet one another at 90 degrees. I have previously built a small 180 build volume printer using this technique with good results.