Mathematics of flat-pack box design and assembly

Does anyone know if there a name for the subject of flat-pack box design, and what is/are the corresponding mathematical methods applied for modelling the assembly from 2D (flat) to 3D (assembled)? Presumably these are used in box design processes.

Background: I'm trying to design a certain type of box, and slowly coming to the conclusion that I may need a more analytical approach.

Thanks for your input!
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Thibault St john Cholmondeley-ffeatherstonehaugh the 2ndCommented:
A two dimensional version is called a 'packing problem'. There are probably three dimensional versions possibly under the same heading. I had a quick look but didn't see any relating to boxes.
It sounds a tough assignment.
xeniumAuthor Commented:
Thanks. I googled the "packing problem" and it seems this is about how to pack known objects into a known space. What I need is more subtle I think, to design the object itself based on constraints such as how it will be assembled.

I suspect I might start with a set of equations defining the constraints, using trigonometry at least. The term "phase space" jumps to mind, not sure if relevant. eg take a simple example of a square piece of card folded in half... what equations define the possible movement of the card? there are two planes which intersect along a line, the angle between the planes can vary by any amount, so this is probably straightforward.

But presumably complexity increases substantially as cuts and folds are added...

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xeniumAuthor Commented:
hi Ozo, thanks for that link it looks like the way to go. Leads to some interesting demos eg

Mathematica software is probably what i would need on the technical side.

Agree with d-glitch it's probably more art than science, but then again on the front-line isn't it all art ;-)
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