There's a 3D graphing application for TI-83+ series calculators [1] and an easter egg was that it could plot the head of a duck. [2] (it had the equations for the surfaces in the code somewhere, presumably.)
The first thing that came to my mind when I saw that you can upload an equation on this site is, 'I wonder what the equation is for a duck?'
I don't know. However I would guess it's because the main portion is a sphere and that's easy enough to show on the 96x64 pixel screen of the 83+ series calculators.
I did this for a bathymetric map, but I it was hard to get the resolution I wanted, I used a laser cutter that was too small, so someone just exported the model and showed me it in AR which actually was a better experience. So this works well for small projects, but it gets insanely work intensive to do for larger projects.
This is super cool! One suggestion I have is to try to optimize the arrangement of the cut-outs to use the paper more efficiently. In some cases I think up to 2x the cut-outs could fit on a page.
You may also want to consider trying to arrange the cut-outs so that the flat edge aligns with the flat edge of the page. Might result in less cutting for the user.
The first thing that came to my mind when I saw that you can upload an equation on this site is, 'I wonder what the equation is for a duck?'
[1] https://www.detachedsolutions.com/graph3/
[2] https://www.detachedsolutions.com/features/graph3-3.gif