I modeled and 3D printed a series of Tesseracts (or Hypercubes) rotating in 4D space. This is the result:
This was one of the most enjoyable projects of the semester. I learned a lot about 3D (and 4D) modeling and different kinds of printers.
A tesseract is a 4-dimensional cube. Much like a 2D creature contemplating a 3D cube, it is very difficult for us as 3D creatures to understand 4D objects. They can be understood mathematically but is challenging to represent visually. One approach is to make what is called a "perspective projection" of the 4D tesseract down to 3D space. This is analogous to a 3D graphics pipeline that will project a 3D object to 2 dimensions to display on a computer screen. The only difference in this case is I used a 3D printer for the final output.
The below animation shows a tesseract rotating in 4D space. Parts of the tesseract get bigger and smaller as they move closer and farther away in the direction of the 4th axis.
I modeled several versions of the hypercube as it rotates around a plane (yes, plane!) and 3D printed each of them. The modeling and math were done with Python and Rhino's SDK. I wrote documentation explaining the math and code.
Here are my blog posts for this project showing the design progress: