Whitney Umbrella

thingiverse

Inspired by Tanya Khovanova's blog post https://blog.tanyakhovanova.com/2023/02/whitney-umbrellas/. See her post for explanation of the mathematical significance and some cool crocheted realizations. The .stl has ridges that highlight the straight lines embedded in the surface. I used custom support enforcers (slab or painted in the PrusaSlicer). It might also print cleanly without supports if rotated to put a parabolic edge on the build plate. It probably would need a raft in that orientation to get more contact surface. After printing, I found another Whitney Umbrella thing: https://www.thingiverse.com/thing:4402629 Pics 4 and 5 (whitney2.stl) is two Whitney umbrellas, joined "X" to "X" where the umbrella intersects the bounding plane in two crossed lines. Parameters were chosen to make the lines cross at right angles in this plane, so one umbrella could be rotated a quarter turn and still meet the other. The result is a 1-sided surface.