Why are egg cartons 2×6 instead of 1×12 or 3×4?
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A 1×12 design creates a product which is very long. It would be hard to fit a carton into a grocery bag, and holding it from one end could cause the torque from the eggs’ weight to overcome the strength of the paper, breaking the carton.
A 3×4 carton doesn’t have these problems, but a 2×6 carton is narrow enough to fit in the door of many refrigerators, while a 3×4 carton wouldn’t.
1×12 would not be that stable and can easyfall over if the egg was standing, with eggy layin on the side requiring bottom area increase. It would also be impractical long, so harder to transport and store the 2×6.
I would guess that 3×4 is not common because you can store them as efficiently. Regardless of whether you store them in a refrigerator or on a shelf, the depth is closer to 6 eggs than 4. I would purchase a large pack for exampel 18 or 24 where 3×6 and 4×5 are common and cut them down and try the size
That said 3×4 cartons do exit you can order them https://www.eggcartons.com/products/egg-carton-vintage-printed
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Other sizes do exist, including 3×4, and where I live, 10-egg (5×2) cartons are more common than 12-egg ones. So it’s not as black-and-white as you’re assuming in your question.
It’s true that 1×12 doesn’t really exist, because that wouldn’t be strong or stable enough – the carton would tip over very easily, and buckle/snap under its own weight if you didn’t hold it carefully.
As for 3×4, as I said this does exist but it’s probably less convenient for stacking, since dozen-egg cartons are often stocked and sold side-by-side with half-dozen cartons which are 3×2. If you use a two-row design for both, the cartons have the same width, and a dozen-egg carton will be pretty much exactly twice the length of a half-dozen carton (sometimes a two-dozen package will actually just be two half-dozen cartons stuck together). And if you sell 24-egg packages too, they’re nearly always 6×4 so again a nice multiple of the smaller sizes. But again, this is not a hard-and-fast rule, and it’s not like 3×4 cartons are impossible to work with. Besides, as I said, there are many other possible sizes that aren’t even multiples of a (half-)dozen, like 10 (2×5), or 15 (3×5) or 18 (3×6) or 20 (4×5) and so on.
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