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The Klein Bottle

About the Klein Bottle:

History: First described by German Mathematician Felix Klein circa 1882. (source: Wikipedia)  Wikipedia describes the Klein Bottle as an example of a non-orientable surface.  A two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined.  Informally, it is a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down. ...

For my part, I am looking at odd-ball geometric projects that I can print in 3D.  There have been other geometric objects so far, but this Klein Bottle sort of struck my fancy.

Notes about the 3d printer.  I am using a consumer grade FDM (fused deposition modeling)  printer based on the Pruisa RepRap design. Cost of this printer was low.  Cost of the filament, either ABS or PLA, is not expensive either.  What this does is allow me to produce a solid object I can hold in my hands created from what I draw within my CAD software.


Klein Bottle #8.
material: ABS 
Process: draw solid model in CAD, 3D print, Post print processing

Notes on Klein Bottle #8.  This object takes 24 hours to print.  Post-print processing takes an additional 30 hours.  Some of that is actual work involving debur and then sanding its exterior surfaces.   The rest of the time is consumed in an acetone vapor chamber.  The acetone vapor melts the outer surfaces of the object and, when done properly, produces a smooth shiny exterior surface.  I should also note that when the acetone vapor process is carried out improperly the object can be destroyed with its surfaces melted down too far.

DSC_2951.jpg (142123 bytes) hint: click on thumbnail to view image full size. 

DSC_2954.jpg (161051 bytes) DSC_2957.jpg (137701 bytes)  DSC_2973.jpg (602339 bytes) DSC_2974.jpg (385922 bytes) 

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Below: quick shade views of the solid model used on this Klein Bottle #8.

CAD program: Rhino Ver. 5 


Klein Bottle #5
Material: PLA
Process: Model in CAD, 3D print, minor debur

KB5concept_5.jpg (99309 bytes) KB5concept_6.jpg (93508 bytes) hint: click on thumbnail to view image full size.

Above: Cad model of the subject in shaded view.  Software: Rhino 3D V5

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Above 7 images are of the actual printed Klein Bottle