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Can someone describe the steps to make a paper cube from a sheet of cardbord with squares (3x5) - the second and forth squares from the second row are removed. The sheet looks like this (black boxes are cut):

image

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Why and how do you want to make a paper cube out of this? You only need $6$ squares, and it doesn't work particularly well if the squares are connected in a circle. –  TMM Dec 14 '12 at 1:25

2 Answers 2

up vote 6 down vote accepted

Instructions:

Dashed lines are valley folds (up towards you)

Dotted lines are mountain folds (away from you) box

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+1 Cool, Ben. Could you make me an origami sewing machine? How about a mirror that folds up into a compact package and then once in orbit it self-unfolds? This sort of stuff impresses the heck out of me. –  Rick Decker Dec 14 '12 at 3:23

Well, it took a bit of cutting, folding, and cursing, but I think Ben's solution actually works. Heck of a lot of waste, though, so since you didn't specify what we could and couldn't do, how about this? Cut all but one square in half along its diagonal, giving you 24 right triangles. Collect these into six groups of four and glue each group together so that they form six squares where the boundaries of the squares are the diagonals of the triangles. Now you have the left, right, front, back, top, and bottom sides of a cube, each having edge length $\sqrt{2}$. Throw away the square you didn't cut at the start, or cut it into six rectangles and glue one on each face for decoration.

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