Home

> 4D Maze Game

  Download
     |
  The Idea
  In the Maze
> Notes
  Reference

  The Fourth Dimension
  Can You See It?
     |
> The Tesseract
  The Tesseract, Part Two
  The Hexadecachoron
     |
  How Much Space Is There?
  Rotations
  How to Point
  How to Orient Yourself
  Volumes
  Walls Are Opaque
     |
  Some Mathematics
  Bibliography

The Tesseract

The tesseract is the four-dimensional analogue of the cube. Just as a cube has six faces that are squares, a tesseract has eight faces that are cubes. You can see all eight faces in the following wire-frame model. (The large cube is the closest face.)

   

I like to think of the faces as being organized into pairs. There are back and front faces,

   
   

left and right faces,

   

top and bottom faces,

   

and inward and outward faces.

   

Since the faces are opaque, you can't see all eight of them at once, but if you take off the front face, you can see the remaining seven.

Tesseracts are important because the entire maze is constructed out of them. We saw one when we looked at the forward passage in the tour, for example.

If we really understood the four-dimensional world, we would know that the eight faces all have the same size and shape, and that together they enclose an interior that is not the interior of the large cube.

next

 

  See Also

  Bibliography
  The Hexadecachoron
  How Much Space Is There?
  The Tesseract, Part Two
  Walls Are Opaque