In my line of work, I do a lot of stacking and packing cuboids of various proportions. Recently I was tasked with finding a stable arrangement of 5x6 units per layer using 2x3(x1) unit blocks, and this wasn't so difficult.
Nonetheless I was interested to see if there was any maths done on this kind of stacking (with blocks of certain proportions, allowing for rotations and translations). What field of mathematics is this? How can the stability of a stack be quantified (think jenga blocks stacked vertically at alternating orientation versus not)? How does the question change if you allow packing efficiencies below 100%? What if you have two or more different kinds of block, possibly varying in vertical measure?
With 2x3 unit blocks, I was able to come up with a 4x5 arrangment with 90% efficiency, a 5x5 arrangement with 96% efficiency, 5x6 and 6x6 arrangements both with 100% efficiency. Any larger arrangemnt seems to be possible also. All these arrangements seem stable.
Apologies for this being incredibly vague, but I just can't seem to find any resources on these kinds of problems. Maybe I just don't have the right search terms but I'm coming up short.
Any insights or links are appreciated.