ACME Klein Bottle's Frequently Asked Questions last updated 2022 June 16

Are you serious, or is this some kind of joke?

I do make & sell glass Klein Bottles. I fill orders quickly and guarantee satisfaction. Over six hundred presumably happy mathematicians now own my Klein Bottles.

All the same, since Klein Bottles don't have many practical uses, this Klein Bottle business had better be fun. So fun is what I'm having. This is both my business and hobby.

Who's behind Acme Klein Bottles?

Just me, Cliff Stoll. Nobody else. No management. No employees. No investors. No profits, either.

Are you the same guy that ...

Yep, same guy.

OK, so what is a Klein Bottle?

It's a mathematical surface which has only one side. See So what is a Klein Bottle?

Do you make these Klein Bottles yourself?

Not any longer. I tend to overwork the welds and have burned myself too often. Worse, I take a long time to make a Klein Bottle. To keep prices reasonable, I design the Klein Bottles and make the first few, then I turn the manufacturing over to professional glassblowers.

How do you make glass Klein Bottles?

Using Pyrex tubing and a glass lathe.

Unlike most art-glass, scientific (laboratory) glassware is made by rotating hollow glass tubing in a flame. The turning machine, called a glass lathe, looks much like a machinist's lathe, except there's a torch instead of a cutting tool. As the tubing turns on its axis, we heat the areas we want to inflate, then blow through a flexible straw, creating pressure inside the tube. This pressure (from my lungs) pushes out the walls of the glass tubing, much like inflating a balloon.

After we get a nice pear-shape, we torch off the bottom. Next, we prepare the inside neck -- we flare a stub of glass (that'll be the bottom flare) and bend it so it'll meet the side. Then prepare the outside loop from another length of tubing. The trick is to assemble the Klein Bottle from three pieces of glass yet make it look like it's from one piece of glass. This means clean, continuous welds, and smooth spline curves throughout. (Scientific glassblowing is also called Lampwork, which is not the same as art glassblowing)

Why Pyrex?

Borosilicate glass (Pyrex is a Corning trademark, and now often refers to non-boro glass) has a low coefficient of expansion, which makes welding pieces easier. All our Klein Bottles are handmade, so we can't get uniform temperatures throughout the bottle. With a small coefficient of expansion, the glass isn't as likely to break while working, annealing, and cooling. Borosilicates have the disadvantage of being a more difficult to work, as they require higher temperatures and tend to vitrify more easily than more common soda-lime glass.

What about your wool Klein Bottle hats?

I spent a year working with three knitters to develop a design for Klein Bottle hats. Now, a group of home knitters hand knit these according to my designs.

Do you make money off this?

Not much. Hand worked glass and hand-knit wool is expensive, and I sell a few every week. Seems that not many people need zero volume, boundary free, nonorientable manifolds. Even so, I occasionally speak on "Low Dimensional Topology for Fun and Profit".

How long have you been making Klein Bottles?".

Over 25 years of making and selling Klein bottles. I first tried making a Klein Bottle while in high school - Hutch-Tech High School in Buffalo, NY - around 1968. After burning my fingers on glass tubing, I gave up. I made several as an undergraduate at SUNY/Buffalo in 1969, then as a graduate student (in 1977), and later as a postdoc in the 1980's. During the 1980's, I made my first "good" Klein Bottle, and experimented with several novel applications for Klein Bottles. I began Acme Klein Bottle in January 1996 and displayed my wares at the 1999 San Antonio joint meeting of the American Mathematial Society. I've been running Acme Klein Bottle since 1996 - over a quarter century of one sided service to mathematicians.

Do you really guarantee these?

Yes. If you're not happy with the Klein Bottle, return it within a year. I'll refund your money. And if it breaks in the first three months (for any reason - even if you drop it), I'll replace it for $10. Every few months, someone calls for a replacement. So far, exactly two people have asked for refunds.

Can I safely send my credit card to you?

Yep. I handle credit card orders over the secure server, Foxycart. No problems and no complaints. I use the "PayPal Payflow" credit card processor. I never see your credit card number - it goes securely and directly to the bank.

I also accept payments via email and PayPal. My "seller reputation" is over 500, but I'd rather be known for my reputation in the field of mathematics. (My Erdös number is 3)

What's your privacy policy?

I treat my customers as I would like to be treated: I keep your information confidential. After you order, you'll receive an immediate confirmation email, followed by another email that I compose when I actually send you the Klein bottle. I do not compile mailing lists, give away or sell customer information, or send spam. I do not include your credit card numbers on invoices. I do not retain credit card information, indeed, I never see it (it's encrypted and sent to the ecommerce host, where it's processed and discarded. I see only a "transaction ID" and the card's last 4 digits).

I don't send followup email pushing new products. I do *not* use cookies, web-bugs, trackers, analytic cookies, or web-beacons. Nor do I use the spammy tool "carthook" which pesters people who stop midway through the checkout process. Nope, I don't do stuff like that. Again: I treat my customers as I'd like to be treated ... with honesty, speed, personal service, reasonableness, and a sense of humor.

How do you package these?

Your glass Klein Bottle will be double-wrapped in foamwrap & bubblewrap, then snuggled in air-pillows or packing peanuts (usually cornstarch-biodegradable peanuts), inside an oversized box, with at least 3cm (typically 6cm) between the glass and the box-wall. For larger Klein bottles, I often add additional cardboard reinforcing to strengthen the package. I guarantee safe arrival - if it arrives broken, I will immediately replace it for no charge. (seldom - happened once during 2010, not at all during 2011, once in 2012, none in 2013, none in 2014, twice in 2015, and once in 2016, nonce in 2017, thrice in 2018, once in 2019, and twice in 2020, three tims in 2021.)

I usually take photos of the packing process and will email the pictures to you. This way, you will see the exact Klein Bottle and the exact package which the postman will deliver.

How long does it take to get a Klein Bottle?

I try to ship your Klein Bottle the same day that I receive the order. If an item is listed on my website, then it is in stock. If I run out of an item, I'll update the web page immediately.

In the USA, I usually use the US Post, Priority Mail or First-Class Mail. This is 2 or 3 day service. I'm happy to ship via UPS as well.. I can also send things by UPS Overnight delivery.

Klein Bottles to Canada take about a week via Airmail.

Overseas shipping is typically via postal "First Class International Mail" which is airmail service, and takes about a week to London, England; 10 days to Berlin, 12 days to Sydney and Tokyo.

Faster overseas service is via Express Mail/EMS, which takes 4 or 5 days to Europe, Australia, and Japan.

Some countries take much longer for airmail deliveries: India, Pakistan, Russia, Belarus, South Africa, Mexico.  Sad to report, postal systems of slow-delivery countries seem to  have higher percentages of lost packages.

Incidentally, UPS now charges dimensional weight for all shipments, so it's become expensive to send lightweight packages via UPS. Dimensional weight hits lightweight boxes in this way: Any box with a density under 0.146 gm/cm^3 will be charged as if it has a density of 0.146 gm/cm^3. This is bad news for Acme's customers ... a typical Klein Bottle in an 11x7x7 inch box weighs 1 pound. This shipment has a density of 1 pound/539 cubic inches or 0.05 gm/cm^3 ... so UPS jacks up their price to a "billable weight" of 3 pounds. That's why I recommend using Priority Mail rather than UPS 3-day service.

What comes with my Klein Bottle?

I pack your glass Klein Bottle in bubblewrap and packing peanuts. I include a calibration decal, a calibration certificate/guarantee, a sheet describing what a Klein Bottle is, a warning not to move it into 2-dimensional space, an invoice, and instructions on how to apply the decal. Much of the literature is from my web pages. About four or five pages of topological propagands - if you like my website, you'll like the literature.

Do you barter or trade stuff for Klein Bottles?

Yes -- to my delight, I've traded Klein Bottles for a silicon wafer (thanks Marty!), a pair of chainmail Mobius Loops (from Benjamin Kleber -- WOW!), a Neodymium glass boule, and a boxful of fascinating sliderules (thanks Jackson -- and my smiles to Jerome!). I'm always interested in the mechanical, the old and the offbeat, such as mechanical calculators (especially a Friden Calculator or a Curta calculator), a Teletype machine, an IBM Key Punch, one of those wonderful Teachspin Muon Detectors, or other such physics/math/mechanics puzzles or gizmos.

What do you do with defective Klein Bottles?

Somtimes I have Klein Bottles with minor flaws or cosmetic blemishes, like oven marks, chips, or weld spatter. You can get 'em for half-price -- check the seconds webpage to see what's available. I usually donate these to high school math circles or math camps.

I want a model but you're out of stock...

Sad to say, I don't backorder; I have a hard time just keeping track of orders that I'm shipping today. Best bet is to check into the website every few weeks ... I'll change the webpage when the manifold is back in stock

I need a lot of Klein Bottles...

Wholesale prices on Klein Bottles? Zooks! I usually stock several dozen to several hundred Klein Bottles of each type, and can send them out on short notice. I can offer a small discount for orders over 10 items. Please ask.

Do you make Klein Bottles in Color?

No. Due to environmental laws, Pyrex/borosilicate glass tubing is rarely available in color. Because of this, I can't make bright colored glass Klein Bottles. I once made some colored Klein Bottles using colored plastisols -- I just dipped my regualar glass Klein Bottles into colored plastic coatings. The effect was nice, but after a dozen, I stopped making them - I couldn't easily get uniform coloration.

Do you Engrave Klein bottles?

No. Pyrex glass is pretty much heat-proof -- so laser-engraving machines tend to melt the glass, rather than scoring or etching it. Worse, the glass has compound curves, so the laser beam gets out of focus. I used to engrave these, but the failure rate was so high that I've stopped.

I'm happy to use a Sharpie pen to write your message on the glass (and, perhaps, sign it); alternatively, you can write your greeting or sentiment on the Klein bottle using an indelible Sharpie pen..

I don't like your website - can I redesign it for you?

About once a week, I receive email from someone who offers to remake my website because it "has a very poor design" or "does not offer a pleasant user experience". I'm sorry, but well, I prefer to pay attention to other things.. I don't want flash, html-5, fancy graphics, audio, or even a well-laid out website with an attractive layout and professional CSS. I've written all the content, taken all the photos, and put it together using rather clunky tools. I want a minimalist design that is content heavy and glitz lightweight.

I agree with you: my website is clunky, ugly, confusing, and old.  But it accurately reflects who I am:  clunky, ugly, confused, and old.

If a volunteer fixes up ths website, I'll be left with a sticky situation: who will update & maintain it? The student who writes a nice website probably won't want to fix it during finals. Worse, I'll have to learn the modern tools and advanced techniques that she used to remake my website; probably I'd need to own copies of the software and keep track of source and target libraries. Perhaps if everything were meticulously documented and kept in some git repository.. but it's difficult to get professional programmers to document their code; it's probably impossible to get a volunteer to do so. At any rate, I'd rather pay attention to other things.

In short, if you really don't like what's here, please accept my apologies for this antique website.

As an aside, the e-commerce side of the website is offloaded to Foxycart, who provide high security for ordering. All orders and credit card stuff goes to the secure domain. I never see any credit card information; no sensitive information is sent to or stored on any of my computers. Beyond this, the website works through Cloudflare, to speed content delivery, provide SSL, and protect against ddos attacks.

Can I visit?

Yes, but since I have a family, please email ahead of time. I try not to interrupt meals and evening story hour so we try to limit visits to midmorning or midafternon. There's a map and directions here.

Where are you?

This Klein Bottle business is run out of my home at 6270 Colby Street in Oakland, California ... close to Berkeley and across the bay from San Francisco. Figure an hour from Silicon Valley, what with the traffic jams. A ten minute bike ride from University of California/Berkeley, and a 15 minute downhill drive from the Math Science Research Institute in the Berkeley hills.

When are you there?

 I'll usually answer the phone (510 654 3958) in mid morning, Pacific time. When I'm away for more than a day or two, I'll post a note to the web page. If you wish to visit, please call first, because I often go on hikes with my family.


Did this question and its answer get interchanged?

Would you make one of these for smoking?

Nope. I make Klein Bottles, not bongs, not hookahs. A Klein Bottle is homeomorphic to a sphere with 2 crosscaps. A waterpipe (or bong) needs an input and an output, so it's likely to be homeomorphic to a cylinder, and therefore not a Klein Bottle. It's possible to make something resembling a Klein Bottle into a waterpipe, but I'm not interested in doing so. There's too many other nifty topological shapes to create!

Wait a second -- Klein Bottles only exist in 4-dimensions. You can't make one!


Mathematicians call my glass objects "3-dimensionally immersed Klein Bottles". That is, they are Klein Bottles which have been tranferred into 3-dimensions, without cusps or folds. Also, every small patch of the immersed Klein Bottle is locally Euclidean. A mathematical immersion allows self-intersection, which, indeed, my Klein Bottles do have. My Klein Bottles are non-orientable, just like 4-D Klein bottles, because orientabilty is invarient with immersion.

A 3-dimensional embedding of the Klein Bottle is impossible. This would transfer the Klein Bottle into 3-D without self-intersection.

There is another 3-D immersion of a Klein Bottle (called the figure-eight immersion), but isn't as interesting and even less useful. I may make one of these just for the heck of it.

What's the big deal - doesn't an ordinary wine bottle have one side?

Well, if there's a cork in the wine bottle, then topologically it's a hollow sphere. It has two sides: an inside and an outside. An ant walking on the surface can't get from one side to the other without making a topological change (popping the cork)

If the wine bottle is uncorked, then it's topologically equivalent to a disc (if you assume the glass has zero thickness) or a solid sphere (if you assume the glass has thickness and mass. A topologist will point to the circle at the top of the bottle -- its lip -- as an edge which separates the inside of the wine bottle from the outside. This edge will not disappear if you deform the bottle. So once you make the bottle-walls arbitrarily thin, the wine-bottle becomes a disc. Again, an ant walking on it can get from one side to the other only by crossing an edge.

My glass Klein Bottles do not have a "lip" or an edge. The surface smoothly runs from inside to outside without actually crossing an edge. So if you make the glass arbitrarily thin (it's actually 2 or 3 mm thick), it will not change its topological properties. An ant can fully explore the entire surface without ever crossing any edge.

The nexus -- that pesky circle of self-intersection ought to be located in the 4th dimension. If this were a true Klein Bottle, the two surfaces would cross each other without intersecting. The side loop should jump into the 4th dimension for a few millimeters while it crosses the wall of the Klein Bottle. Too bad I can't demonstrate this...

What do you mean "Zero Volume"?

It's been mathematically proven that any bounded surface in 3-space must divide our universe into two parts: the "inner volume", which is bounded, and the "outer volume", which is unbounded. A true Klein Bottle fails tot divide the universe into an inner & outer volumes. . (this is related to the Jordan Curve problem)

A true Klein Bottle is a 2-dimensional manifold (which pretty much means a 2-dimensional surface). Every small piece of the Klein Bottle is 2-dimensional -- that is, if you shatter a 4-dimensional Klein Bottle, you will get 2-dimensional pieces. However, to assemble these pieces, you need a 4-dimensional space. Since the true Klein Bottle has no edge and only one side (see above), it does not divide the universe into two parts, and cannot enclose a volume. Math folk say that it is a 2-dimensional manifold which exists in R4.

To a topologist, an uncorked wine bottle also has no volume, since it can be stretched into a 2-dimensional disk (two sides, one edge). A sphere is a closed surface which *does* enclose a volume. A rectangle, a cone, and a hemisphere enclose no volume. A Klein Bottle, although it is a closed surface with no edge, does not enclose any volume.

Ignoring the thickness of the walls, my glass Klein Bottles have zero volume because they do not divide the universe into an inside and an outside. They have no boundary. And yes, you can pour water into (and out of) my Klein Bottles, but they are still topologically zero volume.


If you draw the letter "R" on a clear label, then slide that label around the outside of a sphere, when you return it to the same place, the letter looks exactly the same. So a sphere is orientable. On a Klein Bottle, you can slide that label around so that the letter reads backwards. To do this, you'll have to slide the label all the way inside the Klein Bottle (you'll need a long pipecleaner). When it's on the other side of the glass from where it started, the label will read as the mirror image. That's nonorientable.

The Oxford English Dictionary says nonorientable means: "a figure in the surface can be continuously transformed into its mirror image by taking it round a closed path in the surface"

Have you tried other Klein Bottle Immersions? What about the Projective Plane or Boy's Surface?

I'd like to make a glass figure eight immersion, but have not yet had time. Same with other topological manifolds. If you want one of these, please send me e-mail and I'll put the design onto the front burner.

Do you sell perfume bottles or bottles for soy sauce?

Every few weeks, someone asks me to make five hundred perfume bottles or ten thousand aromatherapy bottles. In short, I don't make ordinary bottles ... only extraordinary ones. Your best bet for wholesale glass bottles and plastic bottles is They're a good source for generic glass & plastic bottles and have no minimum order.

Hey - you're selling 10 DeutschMark bills and calling 'em Portraits of Gauss.

Yep. While in Berlin, I was delighted to find the great mathematician on a banknote, so I brought home a dozen and I have a few of these uncirculated and unfolded banknotes for sale.You can't get 'em in Germany anymore. Sadly, many nice looking banknotes were pushed aside by the Euro.

What does ACME mean?

ACME is an English word meaning the peak, or highest point. It's derived from the Greek word <alpha-kappa-mu-eta> meaning mountain peak.

Long ago in America, the telephone book was the supreme reference guide to local businesses. Around 1925, business owners realized that the phone book listed businesses alphabetically. Since the first one listed often received the most phone calls, many businesses were renamed to the beginning of the alphabet. Soon, many small shops were named Acme - plumbers, florists, mechanics, contractors, etc. Many small businesses were named Acme - and by 1938, it had become a joke, seen in the Looney Tunes Cartoons showing Wile E. Coyote using Acme Dynamite. There's a catalog of Looney Tunes Acme products.

As an acrynym, ACME is said humorously to mean, "American Company Makes Everything". It's sometimes is used as a fictional corporation name (in the same way as "John Doe"). It's the fictional detective agency in Carmen Sandiego series. An Acme Thread is a lead-screw with square cross section, often found on piano stools and vises. And, of course, Acme Klein Bottles.

What else are you working on?

I'm working on Boy's Surface, an R-3 immersion of the Projective Plane. With the help of Charles Pugh of UC/Berkeley, I'm working on one of these. It ain't easy -- requires bending non-cylindrical tubing around a tight radius. I'm trying both acrylic plastic tubing and Pyrex glass.

I'm also making a Cup of Tantalus. And a Glass Cadogen Tea Pot. And thanks to a collaboration with Stan Wagon, my Erdös Number is 3.

Can you help me rebuild a 50 year old Friden STW or SBT or SRQ mechanical calculator, or a Friden 132 electronic calculator?

Funny you should ask. Maybe - I'm becoming increasingly experienced in repairing these. Drop a note for more information.

Do you still use callsign K7TA?

Only on 40 meter CW. But that's a different story


How to order an Acme Klein Bottle

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