The area between y=x and y=x^2 is rotated about the line y=1.25. This creates a volume of revolution which looks a bit like a bowl, but with a conical interior and a big hole in the bottom.
This model pairs with Strange Bowl: 16 washers & 16 shells (http://www.thingiverse.com/thing:897934 and http://www.thingiverse.com/thing:897936).
This model was designed and printed by my WLU summer research student Emily Jaekle ('16).
We knew that printing this on the MakerBot would not be successful due to the number of supports. Instead we printed it on the FormLabs Form 1+ printer.
We used the grey color, and adjusted the suggested rotation of the object to minimize supports in the interior. (We ended up deleting some of them.) The printer claimed there were some problems with the design, however it seemed to print OK.
Update: we have also printed this shape on the ProJet 260 powder printer. It is colored red on the inside and blue on the outside. Thanks to Dave Pfaff for his help with this.