Origami Hexahedron

Several interesting geometric shapes can be constructed from origami by folding several pieces of paper into a parallelogram with pockets. To build an origami hexahedron you will need three of these shapes with three different colors.

Folding a piece of origami paper into a parallelogram.

With the colored side face down, fold and unfold the paper in half. Then fold and unfold each half in half.

          

Fold the bottom left corner up and the top right corner down.

At the bottom left corner, fold so that point A hits the first horizontal crease. Repeat with the top right corner. These folds bisect the 45 degree angles made by the previous folds.

                          

Fold the paper in half along the middle horizontal crease.

Fold the bottom right corner up until it touches the midpoint of the top side.

Fold the top left corner down to the midpoint of the bottom side in the same manner as the fold of the previous step. Your figure will then be a parallelogram. You may have a small gap of white in the middle. The smaller this gap is the better your shape is constructed. Tuck the two corners into the corresponding pockets. Your shape is now complete.

To help build geometric figures from these shapes, perform the remaining folds. First, fold the figure in half along the line drawn as a vertical line in the picture above. This line goes through the small gap. Make this fold so that the pockets remain on the outside; fold so that the pockets move away from each other instead of coming together.

Next, fold the right bottom corner back until it is over the top left corner. The fold you will make is drawn in the following picture. Compare this picture with the previous one. Repeat this fold on the left bottom corner.

The following picture indicates these final folds.

Building the Origami Hexahedron.

Make three parallelograms with three different colored sheets of origami paper. To assemble the resulting figures, put the corner of color 2 into the pocket of color 1, as in the following picture.

Next, rotate the figure 90 degrees clockwise, and put the corner of color 3 into the pocket of color 2.

To form the hexahedron, begin to fold color 3 back along the fold line indicated below. At the same time, bend the color 1 corner marked with the circle below into the pocket of color 3 indicated by the arrow. This will form a corner of the hexahedron.

To complete the figure, place the three remaining corners into the corresponding three pockets. You should find that each corner fits naturally into just one pocket. A sign that your finished hexahedron is correct is that each triangular face should consist of two colors, that two corners are surrounded by three colors, and the remaining corners each have two colors.