HOW TO MAKE A FLEXAGON 1. Divide your paper into three rows of four equal columns. The columns have to be the same size, but the rows do not (see pattern at right) (One Side) (Other Side)   2. Number the spaces according to the pattern. Be careful to position the right and left sides of Face 3 correctly 3. Cut on the solid lines and score only the vertical dotted lines. 4. Start with the "Other Side" that has the number "4" spaces on it. Lift up the two center spaces and fold them up and over to the right (Fig. 1). (Figure 1) 5. One space will extend over the edge. Tuck this underneath (Fig. 2). (Figure 2) 6. Fold the "4-2-4" column on the left side up and over to the right so that there are no "4" spaces showing and the "3-1-3" column appears. This creates an empty single space in the center (Fig. 3).   (Figure 3)   7. Fold the "3-1-3" column up and over to the right so that only Face 2 is showing (Fig. 4). (Figure 4) 8. Turn the structure over and tape the two center spaces together (Fig. 5). Clear plastic sealing tape works well. This is Face 1. (Figure 5)

HOW TO OPERATE A FLEXAGON 1. From Face 1, turn the flexagon over so Face 2 is showing (Fig. 6). (Figure 6) 2. Fold the outside edges back and down so that they meet. (Figs. 7a, 7b) (Figure 7a) (Figure 7b) 3. Pull the center fold apart to reveal Face 3 (Fig. 8). (Figure 8) 4. Again, fold the outside edges back and down so that they meet. Open the center fold to reveal Face 4 (Fig. 9). (Figure 9) 5. Reverse the steps to back to Face 2. Turn the flexagon over you are back you started. Hooray!!   Technically, this structure is called a "tetra-tetra flexagon" (it has four faces and four sides). There are also tri-tetra (three faces, four sides), hexa-tetra (six faces, four sides), tri-hexa (three faces, six sides), hexa-hexa (six faces, six sides) and many other flexagons. Some go in one direction to a dead end, some return to their starting point and some branch off into different directions. The instructions given here were adapted from "The Mysterious Flexagons" by Madeline Jones (Crown Publishers, 1966).