By Universal Joint Design via Carl Rodenberg under Felix Klein.

There are plenty of amazing math models 3D printed by the Shapeways community that I like but do not fully understand but none seem to be hurting my head with weirdness quite as much as the recent series printed by Universal Joint Design.

The models presented on Shapeways are recreations of a Classical Mathematical Model Collection originally made by hand in plaster in the 1800's. This portion of the collection was originally modelled by Carl Rodenberg under the direction of the famous mathematician Felix Klein. 

The main portion of this research involved recreating a series of 24 cubic surfaces which demonstrate types of singularities possible on a cubic surface. In topology, singularities are opposed to smooth surfaces in that they demonstrate abrupt changes in curvature at their surface.