Here is a quartic surface: a standard mathematical saddle surface with a second color to show the parametrization. This shape has a point (the middle point) at which all partial derivatives are zero, but the point is neither a maximum nor a minimum. It is created in Mathematica by plotting the graph of the function x^2 -y^2 + 1 on the unit square.
Technical notes determined by trial and error (or more accurately error and error and error ad naseam)
-The parametrization lines are created using the Tube command in Mathematica.
-This was printed with neither raft nor supports.
-The blue base pieces is needed in order to make the print work without falling over, the thickness of the white surface is 2, and the thickness of the blue parametrization is 2.5.
-In order to make the blue base pieces, I made spheres in Mathematica and used the hole options in Tinkercad to cut off the bottom half. Do not just leave the sphere intact and assume that the printer will ignore the part below the build plate. This actually seems to stop the printer for a long time and set there thinking about printing the bottom half of the sphere.
-Do not try to print something too steep - it seems that if it's about the same height as length and width you'll be better off. A steep piece can break off the base under its own weight. On the other hand, too wide will give the dreaded overhangs of more than 45 degrees.
-The side walls that are printed on the dual print can topple over. This seems to be a build plate adhesion problem. No consistent solution to this problem.
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