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Background photograph courtesy Philip Greenspun

ORIGIN
This is a model of the standard immersion of the Klein bottle in three dimensions. The u/v gridlines (in my formulation) are thickened, and special care is taken so that at the circle where the surface self-intersects, the grid does not.

USAGE
A physical model built from this description would make a useful teaching aid. It allows people without access to a computer and 3D viewer to turn a Klein bottle around and examine its features.

In addition, the connectivity of the grid creates a few mobius strips of varying lengths between the grid lines.

FABRICATION HINTS
The complexity of this part demands that it be built using some SFF technique.

The shape is just over two units long, and each grid tube is a near-square .04 units on a side. If the part is sized so the side length is 2mm, the whole shape is just under 4in.

STATISTICS
Cross-section rings: 24
Sides per ring: 6
Object genus: 145
Faces (as triangles): 3456
Vertices (as triangles): 1440
Volume (scaled so side length is 2mm): 11.8 cm^3
Surface area (same scale factor): 25.8 cm^2

PART DESCRIPTION FILES
Geomview OOGL file (quadrilaterals)
VRML file (quadrilaterals)
MUG object (triangles)
STL object

INFORMATION ABOUT THE CREATION OF THIS OBJECT
Click here

See my CS284 project-- it's even prettier!

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