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> 4D Maze Game
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The Idea
In the Maze
> Notes
Reference
The Fourth Dimension
Can You See It?
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> The Tesseract |
The Hexadecachoron
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How Much Space Is There?
Rotations
How to Point
How to Orient Yourself
Volumes
Walls Are Opaque
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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.
See Also
Bibliography
The Hexadecachoron
How Much Space Is There?
The Tesseract, Part Two
Walls Are Opaque