I cut these templates in the laser cutter on 5mm acrylic, then place them on a sheet of real or faux leather, and cut the outline and the slits with an X-acto knife. I mark the holes and cut them with a hole puncher then put leather studs on them either with a leather stud press or with a hammer.
I made several sizes to fit different wrists. The number at the top indicates the overall length in centimeters. For example, a bracelet of 24cm shrinks to 19.5 cm and the braided segment from 18 to 13.5cm.
The slit is the narrowest I could do where it accommodates an X-acto knife and the material does not melt on itself on the return pass of the rectangle.
Overview and Background
I once found this concept of a bracelet that folds onto itself from a book by Martin Gardner when I was 14 years old. It stayed with me because of the simple transformations that make a 2D object into a 3D fold. I can no longer find the source.
Lesson Plan and Activity
Children aged 8-13 also enjoy making these bracelets with their hands and then offering them to their loved ones. With children, have an adult cut the slits with an X-acto knife and mark the outline and the holes with a pen, then let children cut them with scissors.
On how to braid the bracelet, that is the mathematical challenge for you to solve, which also makes this an interesting and unusual mathematical gift. To make it even more difficult, don't mention what it looks like when folded, just give the cut sheet of leather and let them figure out what the problem is.
Adding the leather studs also shows children how clothes with snap fasteners are made.
Sheets of leather (genuine leather or faux leather), or even just paper
Leather studs and leather press kit (with snap fasteners, hollow punch, convex stick and concave stick, e.g. this one)