Above is a complex mapping of the real projective plane. It’s a two-dimensional surface, and similar to a möbius strip or klein bottle in that it only has one surface. However, it takes it a step further. While the others can be represented adequately in three dimensions, the real projective plane requires at least four.

What I made is called a Roman surface, a mapping of the real projective plane down into three dimensions. What’s really cool is that it’s also a linear projection of the Veronese surface, a five-dimensional surface representing the collection of all conics.

I’ll be honest, I barely understand any of what I just wrote. My brain stops visualizing after three dimensions and that differential equations class only gets you so far.

What I do know: I have a two dimensional surface that needs at least four dimensions to be represented accurately, which models a five dimensional surface, and I’m printing it in three dimensions.

If that’s not impossible enough, then I don’t know what is!

I found a nice collection of models from Thingiverse to choose from. I initially wanted to do the wireframe, but thought the tiny bridges would be too weak. This made me opt for what’s listed as “surface 3a” on the website, a much denser and more sturdy model.

I was going to do my print on the Form 2, but the print failed to adhere to the bed. I didn’t realize this, even halfway into the print, because the actual printing is backloaded; forty layers in the first two hours, four hundred in the next two. Four hours after I start and progress has gone backwards: now I’m working with Thomas to filter the resin and reset the machine.

As a failsafe, I started printing the same model on one of the  little FDM machines while the resin was filtering. I thought FDM was slow until I tried SLA; the 4-plus hour print in the Form 2 was done in 40 minutes on the M2.

I had disabled internal supports because there was no way to remove them. Plus, the shape was fairly sturdy on its own. The bottom supports came off fairly easily, but still left the scratchy surface. I started with another print and did a bit of research (googled “PLA postprocessing,” first link) on how I could smooth down the part. The results of my experiment:

 

I may have got a bit impatient with the heat gun and may have turned the temperature up a little too far and may have melted my shape into a nice lump of plastic goop. Lesson learned: PLA makes a great bouncy ball when it’s about 60°C! Cool enough to hold if you keep it moving and still has a good amount of give, but it won’t completely deform!

Like a dog, I quickly lost interest in playing with my new ball. I began browsing through some of the other parts people had been printing and saw some very thin, spindly structures. I thought I’d give a wireframe (just “surface” on the Thingiverse) a shot and whaddaya know:

 

It turns out that FDM is alright at making the spindly bits work after all. I had turned off all supports, save the raft, because I wouldn’t be able to pull anything off without breaking the delicate structure. I was worried it would collapse in on itself, but the spindly bits also don’t have enough weight to do that. I was so happy with the part that I printed another one to turn in.

By the time the duplicate was done, so was the SLA print.  I pulled it out, ran the bath, cut the supports, and was very underwhelmed:

The supports left ugly marks on the piece, worse than FDM. Some were internal and couldn’t be removed. I was somewhat disappointed, but glad I had been working on the backup the whole time. That saved me a lot of trouble and stress later on.

Besides, the wireframe looks cooler anyway:
EDIT: I initially misinterpreted the instructions and printed two copies on the M2. Turns out I’m supposed to use two different printers to create the same part. Luckily, I still had a whole week before the due date (mainly due to me thinking the due date was a week earlier than it was).

I spent most of that week fighting with the Formlabs. Three days and three failed prints later, I conceded defeat. Something was causing the support base to not adhere to the print bed, even after cleaning the machine and swapping out resins. The whole thing was a very time-consuming and generally frustrating process. I gained a thorough understanding of the hardware and software of the Form 2, as well as a newfound justified hatred for the machine. Five total prints, and one (kinda) worked. Please don’t make me use it again.

That left just the wetlab printers as options. The dimension was (is?) down, and the Objet’s supports would be a major problem to remove without waterjetting my piece to pieces. The Fortus wins by default. The print was fairly straightforward; the only difference between it and the smaller FDM printers was throwing the part into lye for a day to dissolve the supports.

I also reprinted on an M2 again to scale the object up a tad and make it lavender. Surprisingly, it did a better job than the Fortus. Maybe it was the settings (I customized the M2 settings for higher resolution but left the Fortus on its defaults) but the little desktop printer made a smoother, more accurate part than the industrial-grade machine. The only advantage of the Fortus print is that it doesn’t have a clear “bottom” face. Each side is essentially indistinguishable from the others. On the other one, the side attached to the raft is clear, if not by sight then by touch. On a smaller note, the Fortus print also had fewer stray plastic strands than the M2 print. I touched both pieces up with the scalpel to remove the worst of the stray extrusions, spending some extra time removing little raft bits and errors on the bottom of the lavender piece.

Overall, I’m satisfied with my parts. I learned just how capable the desktop printers are, how the Fortus works, and to avoid the Formlabs at all costs.

Coming to a gumball machine near you: