Zippable Klein Bottle

Klein bottles are a realy interesting piece of geometry in topology. There are so many cool and interesting variations of Klein bottles that people have turned into crafts such as scarves, glass ware, and puzzles. This Klein bottle is based off of an idea from woollythoughts.com to make a zippable Klein bottle. I thought this was such a cool idea that I decided to make my own version and share it here on instructables.

There aren't a lot of materials for this project, all of which are easy to find at any craft store.

For this project you're going to need:

- 1 30in zipper

- Sewing pins

- Needle and thread (or sewing machine if you prefer)

- Pen (for marking the fabric)

- Scissors

- 2 different colored sheets of fabric (approximately 30x30in of fabric per color)

(I used two old jean legs of different colors)

- A printout of the Mobius pattern

*Special note: Make sure that the zipper can be unzipped all the way down into two halves (I used a sports zipper which seemed to work just fine)

To start, lay the pattern over fabric (a) and mark the outline of the pattern 4 times on the fabric. Don't mind the shaded edges, they are the parts that you fold over to get a nice hem line. Cut out all 4 pieces. Do the same to fabric (b) so that you have a total of 8 cutouts of the pattern, 4 of each color.

This part can be a little tricky, but I will explain it as best as I can. Unzip the zipper all the way so that you get the two halves of the zipper. These will make up the two Mobius bands. Hold the zipper so that it creates a loop. Twist one of the sides to create a Mobius band. Now holding the beginning, we have to slide the zipper along the edge until it reaches 3in from where you began. Pin it all the way around so that there is plastic on either side of the Mobius strip. Do the same to the second half of the zipper. They should be equally sized.

Take two pieces of fabric (a) and sew the two long parts of them together. Do the same to the other two pieces of fabric (a). You should then have two diamond-shaped pieces of fabric (a). These two will go together face to face to create all the sides of the Mobius band. Do the same to fabric (b) to get a total of 4 diamonds 2 of each color.

Then sew the two small ends of the fabric together of the same color so that you get two pieces that look like the diagram.

Now we need to pin the fabric inside of the zipper seams. To do this, first find one of the long seams and fold the edge over about a centimeter. This middle part should be right in the middle (1.5in) of the 3in gap of the zipper twist. Put either side of the zipper on either side of the fabric (making sure to fold over a centimeter for a nice edge) and pin it all the way around. Ignore the somewhat pointy edges, they don't affect the final model. This takes a lot of patience, so take your time and be careful not to poke yourself with the pins. (Remember that a mobius band only has one side, so all you have to do it keep pinning the edge all the way around until you get back to the beginning). Do this for both pieces of fabric and both zipper twists. When you get to the end, just sew the two small end parts together to finish your model.

A Klein bottle is a topological figure that mathematically has only one unbroken side that folds inside of itself. We have made two identical mobius bands that have a large side and a small side as well as a gap for the model to go inside of itself. Take the two bands and connect the ends as you would a normal zipper. Start zipping it up until you reach the very end of the zipper. This can be a little tricky at first, but if your mobius bands are correct they should work fine. After a little practice you should see a Klein bottle form. Using two colors of fabric makes the model even more interesting because you can see exactly where the model splits in half to create the two mobius bands. This model is a really cool hands-on topology project that isn't too hard to make as long as you are patient enough.