The cube is a beautifully simple shape and one that we see every day. To make one from a square piece of paper can be quite difficult though, depending on what criteria one follows. Being very picky about it, I decided that my cube should:

• have no seams or creases showing on any of the faces
• have no edges that open up allowing one to see inside the cube
• use as much surface area of the paper as possible

The ones shown here meet all of those critera. It is a single square piece of paper divided into a 4X4 grid, with diagonal creases in a few spots that are tucked away inside the cube. There are no seams on any of the faces and no openings on the edges.

If you'd like to try your hand at folding this cube, instructions are now available.

Alas, I have found that I am not the first one to design this cube. I found another one online that works exactly the same way (Kasahara and Takahama 1987, pp. 58-59).