Can you make a single cut to a cube to make a regular hexagon? If so, how? And what length are the sides of the hexagon if the cube has sides length 1?
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Well, perhaps unsurprisingly the answer is, yes you can. Cut through the centre points of the sides like below.
If the cube’s side is length 1, then the hexagon’s sides are the longest side of right angle triangles with side length 1/2. So using Pythagorus, its length is the square root of 2 x (1/4), or √2/2.