A Tesseract Walkthrough

Now that everyone has reviewed the introductory material on this topic, it is time to actually work on navigating within a tesseract. As previously stated, a tesseract can be "unfolded" into eight (8) cubes in the same way that a paper cube can be unfolded into a calvalry cross. Now, having determined the vertices of the cubes in the method described previously, we end up with a table looking like this:

5	4	12	13	7	6	14	15
7	6	14	15	3	2	10	11
3	2	10	11	1	0	8	9
12	14	10	8	13	15	11	9
4	6	2	0	12	14	10	8
5	7	3	1	13	15	11	9
5	7	3	1	4	6	2	0
5	4	12	13	1	0	8	9

This is not terribly informative at this point. However, when the eight cubes are drawn out, the results are more informative. Please take a moment to review the below image, and note that I have left the eighth cube out of the drawing for clarity:

This drawing was created by sketching out the eight cubes, arbitrarily taking three cubes and stacking them on each other. For simplicity, I refer to these cubes as the base column, with the cubes being numbered (from the bottom) Base 1, Base 2 and Base 3. Similarly, the other four cubes shown are designated North, South, East and West cubes. The final cube (not shown) is referred to as the Transfer cube.If you look at the drawing, you will note that the cubes have been arranged so that the faces that touch another cube have the same numbers on their faces. For example, the east cube touches the Base 1 cube along the face 5,4,6,7 and the west cube touches the north cube along the face 2,6,0,4.

Now here comes the tricky part. The North, South, East and West cubes are not fixed in their positions. Note that these can be "rolled" up the Base Column to touch the central or upper cubes as well. This does not reflect that they are actually rolling, but that they are actually touching those cubes simultaneously. Let's take an example. Suppose that a visitor to the bottom Base Pillar cube decided to walk west into the West Cube. The visitor decides to climb up to the ceiling and go through it. From an outsiders perspective, the visitor would now be standing on the 6,7,3,2 face of the second cube in the Base Pillar! Someone who has watched the conclusion of the movie Labyrinth will immediately see the possibilities of movement inherent in the topography of a tesseract.

To clarify, now that the cubes for this example have been labeled we are left with the following table:

Base 1	5	4	12	13	7	6	14	15
Base 2	7	6	14	15	3	2	10	11
Base 3	3	2	10	11	1	0	8	9
East	12	14	10	8	13	15	11	9
North	4	6	2	0	12	14	10	8
South	5	7	3	1	13	15	11	9
West	5	7	3	1	4	6	2	0
Transfer	5	4	12	13	1	0	8	9

Next blog will detail the transfer cube!