It's worth remembering that national only have a lower rebate on the same side as the upper rebate.
Yes, on the
standard National plan that I've seen, the side walls are 3/4" thick but front/rear walls are only 1/2" thick at the top and bottom, due to the rebate. For a truly turnable square box the box would have to be roughly 8 5/8" instead of 8 1/8", am I right?
Some larger square boxes don't have the rebate problem, e.g. many poly hives that are square have thicker walls anyway.
I think a square box is closer in shape to that of the bee cluster, and that the volume of air that they have to heat is therefore less (particularly the square size of a Warré box) compared to an oblong or rectangular box.
It is true that Warré's box is square due to that reason, but that is also why Warré's box is so small. If the box is wider than Warré's ideal brood nest size, then having a square box looses its naturalness, in terms of Warré's ideas.
Warre's "ideal" box is 30x30 cm. Based on what I've read in his book, a box of 30x50 cm or even 30x70 cm would be more consistent with his findings and principles than a box of 40x40 cm or 50x50 cm.
The main reason is to stop you lifting the frames of the lower box when lifting the frames in the upper box. This can happen when the frames happen to be directly in line with each other and the bees stick them together.
If the frames are in line, then up to 100% of each frame is stuck to the frame above it. But if the frames are placed perpendicular, then up to 70% of each frame can be stuck to the frames above it (and not just to one frame, but all of them). Am I right?
And, wouldn't cross-wise frame placing lead to more brace comb between the tops and bottoms of the frames, where the other frames pass over?