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Picture of How to make a Klein Bottle
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A mathematician named Klein
Thought the Möbius band was divine.
Said he: "If you glue
The edges of two,
You'll get a weird bottle like mine."

This Instructable will teach you how to make a Klien bottle, which is a bottle with no distinct inside or outside; a non-orientable surface. You can read more about them here and on Wikipedia. A Klein bottle is very similar to a Möbius strip, the difference being, to quote Wikipedia, that "Whereas a Möbius strip is a surface with boundary, a Klein bottle has no boundary".
A real Klein bottle could not exist in 3 dimensions though, as it passes through itself without leaving a hole. This is not a "real" Klein bottle, because it cannot exist in our world. This is merely the 3 dimensional expression of the impossible shape.
We have, however, figured out how to rotate a four dimensional object through its dimensions, and a good demonstration of that can be seen here, however I can't seem to find a video of a Klein bottle being rotated through it's four dimensions.
There are alternate versions of the Klein bottle like the "figure-8" shape, or the "Lawson-Klein" version, but in my mind they do not hold as much water as the classic Klein.
 
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Step 1: Tools and materials

Picture of Tools and materials
You could do this with any bottle and flexible or hard tubing, but to minimize headaches and joints in the tubing I decided to go with the following supplies:
Materials:
  • Plastic soap bottle - I found that a Method soap bottle has the quintessential shape of a typical Klein bottle's "body"
  • Silicon sealant - to seal the joints of the tubing and bottle in order to get it water-tight
  • Clear Vinyl Tubing - 5/8" ID x 3/4" OD, purchased at Ace, similar to this
  • Hot glue sticks - for use with the hot glue gun (optional)
Tools:
  • Sharp utility knife - for cutting the tubing and removing burs from your bottle
  • Dremel or other rotary tool - for use with attachments
  • Dremel cutoff disk - for modifying the bottle
  • Dremel grinding and sanding attachments - For shaping the holes of the bottle in order to accommodate the tubing
  • Hot glue gun - If the silicon sealant isn't enough to hold everything together, hot glue is your next best bet (optional
  • Marker - for marking out holes and cuts
  • Heat gun - For help bending the tube *optional*
If I had one available, I probably would have used this larger Method soap refill bottle, with the same shape.
Later on I think I might try the two-layered Klein bottle with the large and small Method bottles, should I get my hands on one of the big ones.

Step 2: Planning your design

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One tricky part about using the clear vinyl tubing was that it got kinks in it if it was bent too far. You need to find a sweet spot between having the tube too long and having it too short in order for it to not get a kink in it.

First, cut a small 1 inch section off the end of your vinyl tube. You'll make this into a template for the hole on the side of the bottle. Put your bottle on a table and bend the tube into its final position above the bottle. It's possible to use a shadow to help you with alignment. (You're probably using two hands to bend the tubing into shape, so either memorize the location of the intersection of the clear vinyl tube and the wall of the bottle, or get a friend to help you with lining the 1" slice of tubing up above the intersection, and using the marker to draw a line that follows the edge of the bottle.) mark the height on the bottle where the tubing crosses it. look at the first picture for an example of this piece.
If you're short-handed and have to memorize the position of the intersection, drop the tube and then place the 1" section where you remember the intersection to be, and mark a rough line on the slice of tubing where the edge of the bottle The pictures might be the best representation of this. It isn't critical that this is perfect, but you should get a good general idea of the placing and angle.
This is necessary so that you have an accurate template for the positioning and size of the hole on the side of the bottle. If it is too high or too low, the tube could easily get kinked or the finished product might be really hard to fill. It's important to get the angle correct so that the hole you cut will fit the tubing and accommodate its angle. If you have a heat gun or way of directing heat at the tube in order to help it bend and stay in place without kinking, just make a curve that looks good! Ideally the tube on mine would've been shorter, but I was limited by the integrity of the tube as a circle.
Mark the tube on the top and bottom where it should connect to the bottle during this step, because you'll already have the tube in the position you like. Note that if your tube is going to go over or under the threads on the bottle, the mark should not go at the point of contact, but at the end of the threaded portion.

for the top connector, If the tube does not fit on the inside or outside of the top of the bottles threads, you need to either sand the threads off or cut the entire threaded portion off. If you're using a very cylindrical bottle where the threaded portion is much smaller than the of the bottle itself, you need to keep the threaded section on and work around it, possibly by whittling your tubing down.
On the bottom of your bottle, trace a circle with the slightly smaller outside diameter as your tubing.

Step 3: Making the cuts

Start your hole on the side with a drill bit in your Dremel. I cheated a bit and when straight to the sanding attachment by angling the barrel and slowly pushing and tilting it until it could fit inside the bottle. Once you can get the sanding barrel into the hole you've made, sand in a slow and consistent circular motion around the hole, avoiding stops so that you don't sand away too much in one area and get a bump.If you traced properly around the angled sample you made, you should cut the hole slightly shorter than your markings; the width of the tube stays the same but the height of your hole changes with the angle that it intersects the bottle.
In a real four-dimensional Klein bottle, this hole would not be necessary. Curse you fourth dimension!

For the top connection of the tube to the bottle, you really lucked out if your tube fits snugly on the inside or outside of the threaded portion. Go ahead and pat yourself on the back for your bottle choosing skills if this is you.
For the less fortunate, those of you who decide that only your threads need to be sanded off and it'll fit snugly, go ahead and bust out the ol' Dremel and attach its sanding barrel snugly. Go ahead and sand the threads off, but do it a little at a time and try the fit. If you're so close and don't want to put yourself through the ordeal described below, you can take your Dremel's sanding attachment to the inside of the vinyl tubing and thin the walls out a bit. For some reason, I thought of this as cheating, but you can make your own choices.
For the poor DIYers out there with a completely incompatible length of tubing and bottle threads, you've gotta cut the threaded portion off entirely. Go ahead and cut the threaded portion off with your Dremel equipped with its cutoff disk, remove the burs with a utility knife, and test the fit. If you have a bottle that slowly tapers to the threaded area, like my bottle, and your tubing is still too wide, you can sand down the hole and make it larger and larger to fit the tube in.

For the bottom connection, simply cut a hole on the inside of your traced circle on the bottom, slightly smaller than the tubing. Sand it slowly with your Dremel to give it a tight fit, as this hole is the most important in its accuracy if you plan filling your Klein bottle with water.

Cut the tube at your marking, straight across, with a sharp utility knife. It doesn't have to be perfect, and you'll trim it up later, but you want to have the basic length of it down.

When you're finished making the holes, you should make sure everything fits where it's supposed to go, and that the tube is kink-free. Make adjustments with the sanding barrel, but keep in mind that it should be a very tight fit, especially at the top and bottom where there's not much contact area between the tubing and the bottle.

Step 4: Sealing

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Sealing the bottle is essential if you want to put liquid into it. For me, the sealant I used also helped to hold everything together.
I probably should have used a dedicated glue to affix everything together, but in the end this sealed it completely and was almost unnoticeable.
Get your tubing and bottle together in their final position. The top connection should have little overlap, but do what you need to in order to make it secure. At the bottom connection, the tube should go through the hole and have excess coming out; you can cut off the leftover afterward. If there's a kink in the tube now, there will be when you're finished, so get just the way you want it.
To seal, I ran a bead of sealant around the perimeter of one hole at a time, followed by running my finger smoothly across it to close all of the gaps and cracks. It might help to gently push the tubing in and out of the bottle, in order to get some of the sealant in the joint itself.
To clean it up and give it a smoother look, I pulled a shop towel over my finger (think fancy person with a napkin) and dragged it across the seal lightly.

If you need more structural support for the positioning of your tube, you should use a glue. A hot glue gun might work well to affix everything together quickly if your positioning requires you to hold it in place, but an epoxy would be bullet-proof. Your design should try to avoid too much stress on the top and bottom joints though, anyways.

Wait the recommended time for all of your glue and/or sealant to dry. I had to wait a day, so I left it in a safe and clean environment in a position that did not stress any of the joints for 24 hours.
When it's dry, make sure all of the connections are strong and gap-less. Then, cut the bottom section that protrudes off using the utility knife. I found it best to angle the knife tip into the center of the tube, so that it profiled the joint more. Be careful not to cut the silicon off or nick it in a way that would compromise it's water-tightness.

Step 5: Filling it!

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The trick is to pour water to the top of the tube that comes out of the bottom, place a finger over the hole, invert the bottle until the bubbling has stopped, turn the bottle upright again, and repeat from the start until you have a water level you're comfortable with.
Alternatively, you could submerge the entire bottle and forgo the filling part, but you still would need to invert the bottle. I didn't have a tall enough sink to do this.
Another way to fill a Klein bottle would be to get a tube that has a smaller diameter than the tube of the bottle, thread it through and into the main body, and then attach a funnel or syringe to the tube to put water in it without needing to have separate air and water exchanges.
In order to add colored water to your Klein bottle, complete the steps listed above, and then place a few drops of food coloring inside the tube at the bottom. Plug this hole with a finger or cork, and then repeatedly turn the bottle end over end until it has all mixed together.

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berky934 years ago
I love mathematical structures, but the klein bottle is easily my favorite. I designed one and had it printed using a 3d printer, figuring out how to create it was a great challenge (mainly because if you create a full klein bottle with no thickness and then thicken the edges to make a 3d, printable object the extrusion doesn't compensate for the intersection point between interior and exterior, so there is a weird "crossing over." To counter this I created the bottle with no thickness like usual, but at one intersection point I had the section I knew would extrude inward be wider than the other section, so when they extruded the edges met up. Then I had to simply delete the polygons in between and weld the vertices. I talk too much :p)

My first one is white plastic with holes in it to see the shape (almost, but not quite wireframe) but I want to make another one that is solid and transparent.
Z.Backas (author)  berky934 years ago
I'd love it if you posted a picture! A Klein bottle has always topped my list of things to make with a 3D printer.
Here's a picture. Not the best shot, but I think you can see what's going on. You can see a 3d view on the product page in myShapeways shop (insert shameless self-advertisement: http://www.shapeways.com/model/116104/magic_onion.html?gid=ug25751 <--yes I called it the Magic Onion. You can see the resemblance, no?)
technicly that one does have and inside/outside because of holes :D
GASSYPOOTS3 years ago
why is tere a hole and fill with a magnetic liquid add a makgnet finish off tube and remove magnet!
I just made this bottle. One trick to get the pipe not to kink and to still retain a tight curve is to fill the tube with sand, seal the ends with wire and tape, fold the tube over itself with the right curve (like one of the breast cancer ribbons) and use wire to hold it in that shape. Boil it for a few minutes then dunk in cold water and remove tape, wires and sand.

For the neck of the bottle I used a piece of wide tubing and a piece of slightly skinnier tubing so that they both stayed firmly in place rather than seal the neck with glue. This allowed me to "open" the neck of the bottle and fill/empty it with ease.

Thanks for posting this instructable!
Z.Backas (author)  evilghostbat4 years ago
That's a really great idea. Months after I made it, the kink only got worse.

It would be great if you posted a picture of your bottle as a comment!
Dr. dB4 years ago
Technically, you oughta fill a Möbius/Klein bottle with something Escher-vescent...
Z.Backas (author)  Dr. dB4 years ago
I was fresh out of them! A faucet was sufficient, fortunately.
joshuatex334 years ago
Even after reading this entire post and all of your comments, im still lost as to what this jug is for... But good on you for revisiting part of history!
Z.Backas (author)  joshuatex334 years ago
It really does not have a purpose. It is a mathematical novelty/demonstration item. Exactly like a mobius strip.
mudchuncker4 years ago
try warming the tube with a heat gun should make the tube easier to bend with out kinking it
Z.Backas (author)  mudchuncker4 years ago
Thanks for the idea, I didn't have access to a heat gun, but I bet this would work well! I'll suggest it in the instructions.
uthus4 years ago
Would it not have been easier to fill the sink and submerge the bottle to fill it?
Z.Backas (author)  uthus4 years ago
Well the thing is that you need the circular motion in order to exchange air for water, with only one inlet. You could submerge it and just rotate it underwater, I suppose, but just submerging it would not work.
use a piece of aquarium airpump tubing and a funnel - thread it round the bend into the core of the bottle, hold the free end higher than the bottle itself - put a funnel into the free end and pour in your water. there will be enough free space for air to escape round the tubing while the core fills with water.
Z.Backas (author)  Madrigorne4 years ago
I thought of this too! I just didn't have a smaller tube, and I also wanted to show how to do it with just the bottle. I'll add it though, thanks!
Flackyto4 years ago
wasting wasting too much water only to fill this little bottle ¬¬
When I was a lad, topology fascinated me. Now I am getting old and grey, please would somebody tell me what a Klein bottle is actually useful for ?
Another use for a klein bottle that I have noticed, simply by playing with one, is to pour out specific amounts of a liquid from a larger amount without a measuring device. This is because to pour liquid out of a klein bottle you must turn it over to let liquid fall into the thinner tube, then right it again to pour it out. So only a specific amount can be poured out at a time.

I don't know how accurate it is or even useful, but it's neat.
they make excellent wasp traps
You genius ! And I'll bet my boots that Doctor Klein never even thought of that !

(I don't gamble, it's just an expression.) (In any case, I might be wrong.)

With Dr Klein's theoretical perspicacity (did I spell that right ?) and your brilliant practicallity and business sense, the two of you could make millions !

Is he still alive ?

Christian Felix Klein (25 April 1849 – 22 June 1925) i think i would trust wiki they say he is toes up.He published two papers On the So-called Non-Euclidean Geometry ( i love that, would so much like to dump the term "so called"on a math teacher )
Z.Backas (author)  bikerbob20054 years ago
I've also seen Klein bottle earings, coffee cups, and wine glasses. In the uniquely mathematical sense of it however, it's almost just become a scientific novelty item and a challenge for glass blowers; it doesn't have a specific use because it's a Klein bottle.
Yahaira19844 years ago
Good tutorial, but dont leave the water running... Turn off the tap dude!
Wasagi4 years ago
But what if it tips sideways :O
Excellent!
gockers4 years ago
I'm writing a story that folds in on itself. I'm calling it "Mobius Dick"
ilpug4 years ago
nice! i might make this into some weird kind of lamp...
Z.Backas (author)  ilpug4 years ago
Great idea! If you want to use the same bottle, method soap also comes in sort of a frosted bottle, which might work nicely to diffuse an LED, if that's what you're talking about. You could also put some kind of murky water in a clear one with a waterproof light.
another iteration of this for practical use would be a vase or cup, but that would require more customized parts.
ilpug Z.Backas4 years ago
I was thinking of combining the klein bottle and this --->

http://www.instructables.com/id/Build-LED-Glow-Tubing/
Z.Backas (author)  ilpug4 years ago
It seems like the hardest part would be to get the center are to glow evenly, but if you fine tuned the solution to get it to work, It could be brilliant! This is on my mind.
Gunnar1204 years ago
I have looked a little at klein bottles a year ago, and I just realized that they must be difficult to clean.
Z.Backas (author)  Gunnar1204 years ago
Klein bottles and mobius strips are a continuing interest of mine as well, and that's why I finally decided to make one! It's not too difficult to clean, I mean you just fill it and shake it with some soap, if you needed to. I don't really put anything in it that would make it dirty per say, just water and coloring.
Yeah, have you seen the price of 4-dimensional bottle brushes!
Not to mention trying to drink from them.
76543214 years ago
I had method hand soap once... smelled terrible. Cool instructable.
i agree with that one... thats why i get them out of the recycling
Z.Backas (author)  Scurvymcdiggle4 years ago
Luckily scent has not yet figured out a way to bound that fourth dimension.
SHIFT!4 years ago
Simple yet effective! Nice Work!
Z.Backas (author)  SHIFT!4 years ago
Thank you! It was a lot of fun to build.
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