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Mathematical Model Collection originally made by hand in plaster in the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.
Currently portions of the collection are on display at the University of Goettingen Department of Mathematics, The University of Hong Kong Department of Mathematics, The Institute Poincare in Paris and at the Museum of Mathematics in Manhattan. Check out more images on their Flickr Stream and you can purchase the models from their Shapeways shop.