# The Tesseract (or Hypercube)

## A guided demonstration

The Tesseract is a guided demonstration of how we can visualize rotation in four dimensions. The demonstration begins with the rotation of a single point, and builds up step by step to the four dimensional analogue of a cube, called the tesseract.

Important note: This demonstration relies on animations to illustrate the relevant ideas. These animations are fairly large (about 500 K on average) and thus will take a long time to download without a high-bandwidth connection.

## How to make a tesseract

Start with a point. Make a copy of the point, and move it some distance away. Connect these points. We now have a segment. Make a copy of the segment, and move it away from the first segment in a new (orthogonal) direction. Connect corresponding points. We now have an ordinary square. Make a copy of the square, and move it in a new (orthogonal) direction. Connect corresponding points. We now have a cube. Make a copy and move it in a new (orthogonal, fourth) direction. Connect corresponding points. This is the tesseract.

What new (orthogonal, fourth) direction, you may ask. Well. . . any other direction! That is, to visualize the tesseract, there doesn't need to be a physical analogue of the fourth dimension. All you need is your imagination, and we hope you will enjoy this demonstration of just such an approach.