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Explanation:

On a piece of paper, draw horizontal a line. This is for the 1st dimension. Note that this line is dividing the available 360 degrees by 2, leaving 180 degrees available. For the 2nd dimension, draw a vertical line. This line divides the remaining 180 degrees by 2, leaving 90 degrees available. For the 3rd dimension, draw a diagonal line. Again, this line divides 90 degrees by 2, and 45 degrees left.

OK it was standard up to this point. My idea is: for the 4th dimension, all we have to do is draw a line that divides the remaining 45 degrees by 2! (as shown in the above picture)