How to make a Klein Bottle

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.

Step 1 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.

Comments

[berky93]

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]

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.

[berky93]

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?)

[GASSYPOOTS]

technicly that one does have and inside/outside because of holes :D

[GASSYPOOTS]

why is tere a hole and fill with a magnetic liquid add a makgnet finish off tube and remove magnet!

[evilghostbat]

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]

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. dB]

Technically, you oughta fill a Möbius/Klein bottle with something Escher-vescent...

[Z.Backas]

I was fresh out of them! A faucet was sufficient, fortunately.

[joshuatex33]

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]

It really does not have a purpose. It is a mathematical novelty/demonstration item. Exactly like a mobius strip.

[mudchuncker]

try warming the tube with a heat gun should make the tube easier to bend with out kinking it

[Z.Backas]

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.

[uthus]

Would it not have been easier to fill the sink and submerge the bottle to fill it?

[Z.Backas]

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.

[Madrigorne]

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]

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!

[Flackyto]

wasting wasting too much water only to fill this little bottle ¬¬

[ElectroFrank]

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 ?

[berky93]

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.

[bikerbob2005]

they make excellent wasp traps

[Z.Backas]

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.

[ElectroFrank]

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 ?

[bikerbob2005]

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 )

[Yahaira1984]

Good tutorial, but dont leave the water running... Turn off the tap dude!

[Wasagi]

But what if it tips sideways :O
Excellent!

[gockers]

I'm writing a story that folds in on itself. I'm calling it "Mobius Dick"

[ilpug]

nice! i might make this into some weird kind of lamp...

[Z.Backas]

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]

I was thinking of combining the klein bottle and this --->

http://www.instructables.com/id/Build-LED-Glow-Tubing/

[Z.Backas]

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.

[Gunnar120]

I have looked a little at klein bottles a year ago, and I just realized that they must be difficult to clean.

[Z.Backas]

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.

[Void Schism]

Yeah, have you seen the price of 4-dimensional bottle brushes!

[omnibot]

Not to mention trying to drink from them.

[7654321]

I had method hand soap once... smelled terrible. Cool instructable.

[Scurvymcdiggle]

i agree with that one... thats why i get them out of the recycling

[Z.Backas]

Luckily scent has not yet figured out a way to bound that fourth dimension.

[SHIFT!]

Simple yet effective! Nice Work!

[Z.Backas]

Thank you! It was a lot of fun to build.