My folding experimentation using bands was derived from my experience with circular Origami and particularly the use of the triangular grid that could easily be folded in it.

Here I show one of the simplest folds using the particular geometry of an 'infinite' band. The easiest way to obtain bands of paper is to use cash register paper, which is a bit flimsy, or gummed packing tape, which needs to be licked to stick, so it can be used here dry and the glue is handy for closing the loop.

It is important to begin this folding with a right angle at the end. to achieve this, fold a small section of the end over itself so the top edges line up as well as the bottom. Cut along that line.

1. Fold the band in half. Crease the first width-and-a-half of the fold near the beginning. This will give you a guide line for the next fold.

2. Bring the top left corner in so that it touches the center line from the previous step, at the same time making sure that the fold will touch the lower left corner exactly. You may have to slide the top point along the center line until the fold is right. You have created a 60° angle.

3. Bring the lower left corner to the right along the bottom edge so that the new fold intersects the previous fold exactly on the top edge. You have created a transversal line, perpendicular to the edge of the band.

4. Bring the top end of the new fold down to the bottom edge, making sure that the fold touches the bottom left corner of the band. This creates a 30° angle.

5. Fold the perpendicular bisector of the last fold by joining its ends together. This creates a new 60° angle.

6. Join the bottom left corner of the band to the top end of the last fold to create another 60° angle.

7. Fold the top left area in half by joining the corner of the band with the meeting point of the folds as shown.

8. Make a new vertical fold by bringing the top of the equilateral triangle to the top edge of the band while insuring that the fold touches the lower right corner of the triangle on the bottom of the band, as shown.

9. Join the right most points from the top and bottom together to create a new 30° fold.

10. Fold the perpendicular bisector of the last fold like in step 5.

11. Continue folding in the same manner until you have a total of 12 whole equilateral triangles (six pointing up and six pointing down) in addition to the right angled triangle on the extreme left.

12. Cut off the remainder of the band.

13. Fold the band into a concertina using only the transversal folds (90° to the band edge) and the folds at 60° to the band edges (the shorter oblique folds). Fold the transversal folds into valleys and the angled folds into mountain folds.

14. Using the pre-creased 30° folds (the longer oblique ones), reverse fold the lower areas of the equilateral triangles pointing up and the upper areas of the equilateral triangles pointing down. From the side your paper will now look like a squashed arrowhead pointing away from you.

15. Finally, join up the two ends. there is a half of a triangle overlap. The two flaps can be glued together so that the folds match up.

16. The joined up shape can be used as a bracelet, it can be twisted around itself like a flexagon, it can be flattened around its center of rotational symmetry, etc.

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