TITLE: Is it possible to create a screwless cube made out of 12 individual planks?
QUESTION [7 upvotes]: The planks all have to be identical. But I'm trying to figure out if there is a configuration in which it can be created. Below is an example of a screwless square shape. This cube needs to be able to be assembled, not just fit together.
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REPLY [3 votes]: I believe that the answer is no, and though I am not equipped to provide you with a proof, I can give you a rather lengthy explanation.
When you assemble your two-dimensional example in a plane, the entire reason that it is rigid is because it can't be unassembled in the plane, and to assemble it, you must lift the pieces out of the plane, and then place them back down. However, in order to assemble a cube in an analogous way, you need to be able to pull the pieces into the fourth dimension.
As for @RoddyMacPhee's answer, I don't believe that you can assemble the walls of a cube such that each wall is connected to each other wall using dovetails. Such a cube would be impossible to take apart without destroying it, suggesting that it would not be assemble-able.
TLDR: No, unless you are a fourth-dimensional being.