Tesseract

[Yash]

I read somewhere that a tesseract is to a cube what a cube is to a square. What exactly does that mean? Does this thing include a 4th dimension in some way?

[elfmotat]

My understanding is that tesseract images are "shadows" of 4D cubes in 3D space. Similar to how the following is a shadow of a 3D cube projected onto a 2D space, i.e. your computer screen or a piece of paper.

Tesseract shadows, like the one below, are commonly rotated over time to illustrate its 3D properties, due to the limited nature of having a 2D space to draw on.

 

[mathematic]

http://en.wikipedia.org/wiki/Tesseract

 

See above.