Fairy Crystals are 3D printed Art. They have no purpose, they are entirely useless, but strikingly pretty.
They are a fractal shape that cannot be machined, injection molded, or otherwise manufactured except by 3D printing.
The material is a plastic commonly known as PetG (PolyEthylene Terephthalate Glycol).
Each crystal is a pyramid made of 6 smaller pyramids, each made of 6 smaller pyramids, each made of 6 smaller pyramids, and so on. The 25 millimetre crystals are 3rd order, so they are made of 6 to the 3rd power or 216 tiny pyramids.
This fractal shape is called the Sierpinski Pyramid and its properties make it ideal for 3D printing.
When the fractal repetition is taken to the mathematical limit this shape has infinite surface area and no volume at all. Clearly we cannot reach the limit using real materials, but even at 3rd order there is a lot of surface area and almost no volume.
When a crystal is sliced in the horizontal direction the perimeter is always a single continuous line. This can be seen looking at the bottom side where we see the Crusaders Cross or a Cross made of Crosses made of Crosses. Some Fairies suggest the Cross is a wrong interpretation, the bottom mark is in fact a Pirate symbol for X marks the Spot, marks the Spot, marks the Spot, arrh me Maties pass the rum!
Either way, the fact that the perimeter is a single line is great for 3D printing. The printer can draw each layer in a single pass without lifting the print head and making a little divot or possibly a string. There is very little material used since the volume is small.
The layered topography creates some interesting optical effects. It is 2/3 of a corner cube, the shape of a reflector on your bike or car. Looking through a crystal at 45 degrees shows that same Cross or X that is visible on the bottom. Symmetry is Strange.