3D Printed Tesseract

I modeled and 3D printed a series of Tesseracts (or Hypercubes) rotating in 4D space. This is the result:

Animation of 3D printed hypercube rotating in four dimensional space.

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.

Animation of computer generated hypercube rotating in four dimensional space.

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: