The fourth dimension

A FOUR-DIMENSIONAL FIGURE 129

Now selecting according to the rule every one of one kind with every other of every other kind, we must take, for instance, 37, 2j, 1k, Oh. This point is marked 3210 at the lower star in the figure. It is 3 in the i direction, 2 in the j direction, 1 in the & direction, O in the / direction.

With 3% we must also take lj, 2h, Oh. This point is shown by the second star in the cube Oh.

Fig. 72.

In the first cube, since all the points are 0h points, we can only have varieties in which 7, j, k, are accompanied by 3, 2, 1.

The points determined are marked off in the diagram fig. 72, and lines are drawn joining the adjacent pairs in each figure, the lines being dotted when they pass within the substance of the cube in the first two diagrams.

Opposite each point, on one side or the other of each

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