Double and Triple Klein Bottles
- A Klein Knottle !
... which is a Klein Bottle, and which is not?
By welding together Big Classical Klein Bottles, I've built several double and triple Klein Bottles.
But be careful - one of these is a Klein Bottle, and one of them is not. I will leave it to you to figure out which is the real Klein Bottle.
The Double Klein Bottle looks like an hourglass ... will it work as one? It's been featured on the cover of of the book, "Endless Universe" by Paul Steinhardt and Neil Turok.
The Double and Triple Klein Bottles have all the features of Acme's other quality Klein Bottles -- zero volume, nonorientable, 3-dimensionally immersed, and free from any topological boundary conditions. It's made from genuine heat-resistant Borosilicate glass, annealed, stress-relieved, and cooled well below its triple-point.These are externally linked Klein Bottles; it's also possible to make them linked internally. Carlo Sequin of UC Berkeley has called these Klein Knottles ... sweet!
Both of these styles can be mounted on a wall, in a display case, or placed on a table. With care, you can balance the double Klein Bottle on a flat surface.
The Triple Klein Bottle is roughly an equilateral triangle, 30cm on a side (about 12 inches). The diameter of each of the 3 reservoirs is about 10cm (4 inches) It weighs about 470 grams (17 ounces).
The Double Klein Bottle is about 28cm (11 inches) tall, and each of the two reservoirs is about 10cm (4 inches) in diameter. It weighs about 280 grams (10 ounces).
Hint: One of these is homeomorphic to a Klein Bottle. The other is homeomorphic to a Torus. You decide..
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Cliff last updated this page on September 14, 2023 after restocking his under-house warehouse.