Klein Bottles

You have probably heard of Klein bottles before but may not know that a Klein bottle is like two opposite Möbius strips joined together.

A few years ago we made a knitted Klein bottle hat, in two colours to make it obvious how the pieces joined.

 

I wanted to make a 3D printed Klein bottle in a similar way.

It was trial and error. My first attempt was very messy. I used white supports for blue filament so a lot of white was left on the finished model. The channels on the ‘inside’ of the bottle were too narrow. The walls were too thin so the walls were uneven.

For my second attempt I used supports that matched the model so, when they were broken off, it wasn’t so obvious where they had been. The walls were still too thin.

Perhaps the way to go was to make a model that didn’t need supports. This is much easier to do with a gently sloping surface rather than curved edges.

It worked but the shape was not how you would expect a Klein bottle to be.

I needed a complete change of plan to get a rounded shape. Instead of building the pieces from the bottom up, I started from the flat edge where the pieces would eventually be joined together. The advantage of this was that all the supports would be on the inside so would not really show if they did not break away cleanly.

I could make thicker walls because they were well-supported. I also made wider channels.

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