Sierpiński Tetrahedron

This Sierpiński Tetrahedron makes a great desk ornament. And it's math-y, if you like that sort of thing.

Print Settings

In this print I used:

PLA

0.2 mm layers

Paint-on supports

0% infill (a Sierpiński Tetrahedron has no volume)

Orientations and Supports

There are several orientations this can be printed in. No matter how you do it, you will need to use supports. The way I printed it was having the pyramid balanced on one edge, as it is in the STL file. In this orientation, there are a number of horizontal bridges that must be supported. The easiest way is to use paint-on supports under these bridges. Each of these bridges can be supported directly from the build plate, so there should not need to be any support material built above the part itself.

Another advantage of the on-edge orientation is that it fits perfectly inside a cube. If you wanted to enlarge the part, this will get you the largest size for your build volume.

Although I did not try this, you might be able to reorient the part so that the point of the pyramid is down. Then, by enforcing supports on the bottom layers just to keep the part steady, the rest of the part should not need any supports at all.

After Printing

The part is VERY FRAGILE. You will have to be patient when removing the support material, but with the default settings in PrusaSlicer, it came apart fine. I did reinforce the joints where the largest tetrahedrons meet, but if I were to do it again I would add reinforcement in other areas too. I just didn't want to ruin the perfect mathematical beauty of the thing.

Math

It's a fractal. https://en.wikipedia.org/wiki/Sierpinski_triangle#Analogues_in_higher_dimensions