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the way to turn that 1D line into a 2d square is to project the sides into the 2nd dimension and join the points.
Doing that again, you can make this 2d square into a 3d cube, again by projecting the corners into the 3rd dimension , and violla, a cube.
Now - we live in a 3D universe. To make a 4D object, all we do is project the corners of the cube into the 4th dimension
Ringo
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Check this out if you want to read about N-dimensional cubes.
Hypercubes