Klein Bagel (small)

This is the 'bagel' form of a Klein bottle, a 4 dimensional object with a single surface, projected into 3-space as a self-intersecting solid. The 'bagel' form is a figure 8 spun into a torus, and twisted 180 degrees as it turns so that it forms a single surface object. Only every other strip of the surface has been printed, making 6 separate strips. The surface and the strips are 'non-orientable': the normals to the surface are ambiguous, since the surface curves around on itself like a Mobius strip. 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. Therefore when one attempts to thicken the strips for 3D printing, there is no unambiguous inside or outside. This is solved by making the model in 4 pieces, solidifying each separately, then joining them in pairs and fattening them so that the intersection of the strips also has thickness. The model was created in Mathematica, solidified in Blender, and repaired with Microsoft's 'Netfabb in the Cloud'. The parametric formula can be found in Wikipedia under 'Klein Bottle'.