I interpreted this assignment in a more literal sense than was probably expected, and I wanted to make an object that was actually geometrically impossible. The problem I immediately encountered is that impossible objects are impossible for good reason. Instead, I designed an object that gives the illusion of impossibility when viewed from the correct angle.

The Escher cube was created by M.C. Escher, and usually involves having gaps in the sides of the cube to create the illusion. I took a less common approach, where the impossible side curves around the cube and appears straight when viewed from the correct angle. This approach is a little more forgiving for 3D printing, since it easier to view and doesn’t need to be precisely cut. I designed the part in Solidworks, using a spline curve to generate the impossible side, and scaled it down to fit in the bubble. The finished part can be found in thingiverse with this link: https://www.thingiverse.com/thing:4975670

I first tried to print it with FFF on the Prusa mk 3, and after a few tries and some experiments with support structure, I got a print I was happy with. The biggest issue was that support structure, and removing it after the print was finished. Often I would crack or break the part when I was cleaning it, and the support structure left ugly remnants that ruined the illusion.

To resolve these issues, I scaled up the part and made all the walls thicker. Though this improved printing time a lot, the quality of the part was noticeably better. It’s also easier to see the illusion when it’s larger. Still, a lot of prints I did on the Prusa failed for various reasons. I tried printing two at a time, and for reasons I can’t yet explain that actually helped it print reliably. I also tried doing some prints on the Ultimaker to use dissolvable supports, but I could never get that printer to work and it was almost always being used by someone else.

I also experimented with using SLA. I used the Prusa SL1S printer, and started making some more cubes. In the end I was only able to get one to work. It was beautiful, but all of the others came out looking extremely deformed. I suspect it has something to do with aligning the build plate and making sure the first layers adhere properly. Regardless, it was pretty fun to use such a cool machine. The one print that worked is easily the best of the five, even though one side got kind of squished. The lack of support and visible layers helps the illusion quite a bit.

The 4 parts on the prusa were 9.26g each, which amounts to $0.11 each for the ones made of PLA and $0.19 for the PETG parts. I forgot to record the amount of resin used for the SLA prints, but I estimate around 7mL, which is around $0.56. That amounts to $1.16 for the 5 parts I made, but I made around 3 times as many that failed. I estimate the final material cost to be $3.48.

I also spent around 10 minutes cleaning each part that succeeded, so I could be said that it amounted to an hour of labor. Plus another half hour of lab assistant help to use the printers brings me to an hour and a half of work at $11 an hour. Taking into account money spent on power, maintenance, and other factors, I would estimate that this project cost around $25.