Assuming you're working indoors, the most important consideration when making one of these is to be sure it fits through your doorway. The whole thing is equilateral triangles so you don't have many options for trying to angle it through a narrow doorway.
The Sierpiński tetrahedron is built up in iterations. It's built on a simple tetrahedron made of 4 equilateral triangles. The first iteration is 4 of those tetrahedrons, stacked to form the proportion tetrahedron. That unit times 4 is the next iteration, and so on. One iteration uses 4 tetrahedrons, 2 iterations uses 16, 3 iterations uses 64, 4 iterations requires 256.
This kite is made from paper and bamboo, and is held together with white glue and cotton thread.
(I'll add some in-flight pictures as soon as I can have a photo friend and a gentle breeze at the same time!)
Step 1: Supplies and Equipment
- bamboo skewers
- white glue
- #10 cotton crochet thread or similar thin string made from a natural material
- acrylic paint (optional)
- utility knife with fresh blades
- needlenose pliers
- block of wood or other surface you can damage without consequences
- paint brush
- container for water
- kite flying string
- mitre box saw or other cutting equipment
- masking tape
- dull large eye needle
You're handling sharp stuff, breakable stuff, and splintery stuff in this project. Use the hand, eye and body protection you need to walk away intact.
Step 2: Cut the Bamboo
The bamboo is split for two reasons. The first is that you halve the weight of the kite. The second is that you then have a nice flat side for gluing.
The number of skewer pieces you need is dependent on the size of your kite and the length of your skewers. I was able to cut two lengths from the skewers I had, so after splitting I was able to pull 4 usable pieces from each skewer. To make a 2 iteration kite you'll need 96, to make a 3 iteration kite you'll need 384, for a 4 iteration kite it's 1536.
To split the bamboo hold the skewer with the pliers (never you fingers) and carefully work the utility knife blade into the end. Stand it upright on the block to split it the entire length. You're still cutting near your hands so be very careful.
Some bamboo will split perfectly in half all the way down. Others will not. All of it can be used, so bundle it all together.
After you have all you need plus plenty of extras split, bundle them up tightly and wrap them in masking tape. Mark the length, then cut the bundle down with the mitre box saw. To make a 3 iteration kite that fits through a 29 inch doorway you can make you skewers up to 3.5 inches long.
Step 3: Cut the Paper
Cut one paper piece for each module - 16 for a 2 iteration kite, 64 for a 3 iteration kite, 256 for a 4 iteration kite.
Fold each in half.
Step 4: Glue the Bamboo and Paper
Glue one skewer down the center line with white glue, leaving the ends glueless as shown. Press it in place and allow it to dry.
Then glue the other 4 pieces down, making sure the pairs meet evenly at the ends of the triangles.
Once set, glue the flaps down over the skewer pieces.
Step 5: Tie the Tetrahedrons
Start with the cotton thread and one of the glued up paper units.
Tie a slip knot at the end of the cotton thread. Pull it up tight around the center bamboo piece at one end.
Loop the cotton around the next skewer over, at least 2 times. If you reverse the loop as shown and repeat it 2-3 times it will lock in place. You're really forming a double half hitch on the skewer.
Fold the piece into shape and then tie the next skewer, then tie the original. You want the knots near the ends of the skewers to hold the tetrahedron in shape.
If you're having trouble with the string sliding off try making a very small nick in the skewers with the utility knife where you want the string to set. You only have to convince the string to hold until the next step when you glue it into place.
After doing both 3-skewer ends of the paper, grab one of the thick skewer pieces and tie it with the pairs on the other ends of the paper to form the proper tetrahedron.
Step 6: Glue the Skewers
Add 1-2 more coats, allowing to dry between. Brush the entire inside of the paper as well. This strengthens the paper and helps lock down the flaps you glued down earlier.
Step 7: Paint & Trim
When that's all dry trim the tails from the ties.
Step 8: Tie the Groups
Start with three tetrahedrons, arranged so the paper points the same direction.
Tie them together at the three points they meet.
Add another tetrahedron on top, again with the paper the same way, tying it at the 3 points where it meets others. This forms the first iteration.
To tie the tetrahedrons together:
Cut a 6-8 inch piece of string and thread it onto the needle.
Figure out what pair of bamboo pieces are in the same line (they could have been on long piece.)
Sew in a figure-8 as shown, repeating the pair of stitches 3-4 times. Tie the ends together.
Glue the ties in place, first with diluted glue, then with undiluted glue. Trim the tails.
Step 9: Form More Iterations
Collect 4 of the units made in the last step and arrange them as before, tying them the same way.
Keep repeating this until you run out of pieces.
Step 10: Fly It!
I've had great luck with tying it on the 'open side' (so you can see the insides of the tetrahedrons.)
I've also read that it can work as an air foil, similar to the sails on a sailboat, so it might also work to tie your flying string to the other side (the front in the photo below.)
Keep in mind that this kite is incredibly light weight so it's great for light breezes, but can easily become unmanageable in heavy winds. You built it so if it breaks you can fix it, but it's more fun if it doesn't break!