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.
Please press the
arrow to begin.
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.
For more information . . .
This demonstration is a "petrified" version of a truly interactive
demonstration called NDdemo. NDdemo is part of
NDview, an external module for Geomview.
Geomview is a general package for visualization available from
the Geometry Center software
archive. For now, NDview is packaged separately-- Click here to
download the compressed SGI version of NDview.
This demo was written in March, 1994 by
Olaf Holt at
the Geometry Center. Please
send comments to holt@geom.umn.edu.