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This is a model of Boy's Surface, a one-sided surface with no edges and no pinch points.
This is a modified version of Trapped Outside, without the cut-away track or internal ball. This version has a tiny hole at the three-way intersection point so that Shapeways recognizes the internal space as empty and doesn't charge for it. The hole is so small it will not be printed, and the interior will be filled with support material.
The original design is here: https://www.shapeways.com/model/40473/trapped_outside.html
Without the ball: https://www.shapeways.com/model/237518/trapped_outside__track_.html