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I am not mathematically inclined enough to express this question rigorously, but it certainly sounds like a problem for mathematics.

I was making a cutout from a piece of cardboard to make a box with legs. You can describe the sizes of each section with a model laid out in a plane as seen here.

Since my design has legs and is not just a box the layout is not as straightforward. The sections do not have to be placed in any order as long as everything works out when it's folded. This got me thinking, is there an algorithm for finding the closest packing of a layout like this? It sounds similar to the bin packing problem but with more constraints. Any ideas?

EDIT: By closest packing I mean produce a layout such that the least amount of material is used.

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do we have a specific set of dimensions that we want? –  Vincent Tjeng Mar 4 '13 at 5:19
Yes, the size of the dimensions of all the "parts" are fixed. –  ballaw Mar 4 '13 at 6:40

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