Hyperboloid of one sheet, made taller and thinner than my last model (http://www.thingiverse.com/thing:922323). Three print files here. The hyperbolic-vase-tall.stl file is designed to enable you to use the spiral print function that many printers have. (You don't print the top and bottom layers of the model, instead the nozzle goes around in a spiral, printing the surface 1 layer thick.) The other two files are for traditional versions of the surface (about 2mm thick), one with an equation and one without.
I think adding supports may make the equations print out a little more clearly, worth a try.
Designed in Cinema4D. Made the hyperbola x^2/4 -y^2/9=1 (with asymptotes y=+-(3x)/2), and revolved this around the y-axis. Thickened surface in usual way for regular models. For hyperbolic-vase-tall.stl file giving the 1 layer thick models, simply added a top and bottom to create a closed volume. The printer settings then takes care of the rest.