I solved this by making the cardboard grains run at 45 degrees in all panels of the box. This created the possibility of using locking tabs in both directions. In a traditional rectangular box this means that the joint at one of the vertical edges, which is almost always glued or stapled, can be made with a locking-tab connection, while the top and bottom lid flaps can still be closed strongly. This potentially has a big cost benefit as the extra step of gluing will no longer be necessary. Because I just followed courses about patents at the tu/e, I was inspired to try to protect this design.
I got an investor who liked the simplicty of my design and wanted to try to patent it. I applied my knowledge learned at the TU/e by formulating claims to propose in the application. In the end, our patent attorney found some concerning prior art in their pre-research, so we did not go through with the application. Nonetheless, it was a very interesting and educational experience.
In the context of a laser cutting company I was running, I designed a rectangular transport box, made from corrugated cardboard, that did not require any glue to construct. This is challenging, because corrugated cardboard is very strong in one direction, and very weak in the other: locking tabs and lid flaps of boxes are only strong in the direction of the cardboard grain. Locking tabs in particular, will not hold in the weak direction of the cardboard, causing the box to fall apart.