Hopf Fibration

You have probably heard of a tesseract. In addition to being one of the infinity stones in the Marvel Cinematic Universe, a tesseract is also the name given to a 4-dimensional hypercube. A 4-dimensional hypersphere has its own cool name. It’s called a Hopf fibration.

If a tesseract is to a cube what a cube is to a square then a Hopf fibration is to a sphere what a sphere is to a circle.

While it’s impossible to actually make a 4-dimensional shape in 3 dimensions, there are several common ways to visualize tesseracts in 2 or 3 dimensions. Similarly, the image below is a 2D image of a 3D representation of a 4D Hopf fibration.

Hopf fibration

Pretty, isn’t it?

Here’s an animated visualization:

Animated visualization of a Hopf Fibration