In Scientia Veritas

This video is amazing. And the music too!

In four dimensional geometry, the tesseract, also called an 8-cell or regular octachoron, is the four-dimensional analog of the cube, which is in turn the three dimensional analog of the square. The tesseract is to the cube as the cube is to the square; or, more formally, the tesseract can be described as a regular convex 4-polytope whose boundary consists of eight cubical cells.

Wikipedia: Tesseract

This one is even prettier:

But if you want to appreciate its structure, watch this next one! The author gives a short explanation:

All six rotations of a transparent tesseract. Each rotation that includes the w axis is a minute long, while the other three are each 20 seconds long. This way, you’ll be able to zone out and better visualize the tesseract.

0:00 XW
1:00 YW
2:00 ZW
3:00 XZ
3:20 YZ
3:40 XY
4:00 All rotations in succession