The fourth dimension

196 THE FOURTH DIMENSION

Now let the ochre cube turn out and the brown cube come in. The dotted lines show the position the ochre cube has left (fig. 120). .

Here we see three out of the four points through -2a which the cutting plane Wig. 120 passes, null 7, null y, and

a null 6. The plane they determine lies in the cutting space, and this plane cuts out of the brown cube a triangle with orange, purple and green sides, and null points. The orange line of this figure is the same as the orange line in the last figure.

Now let the light purple cube swing into our space, towards us, fig. 121.

The cutting space which passes through the four points, null 7, y, wh, b, passes through the null r, wh, 6, and therefore the plane these determine lies in the cutting space.

This triangle lies before us. It has a light purple interior and pink, light blue, and purple edges with null points.

This, since it is all of the plane that is common to it, and this bounding of the tesseract, gives us one of the bounding faces of our sectional figure. The pink line in it is the same as the pink line we found in the first figure—that of the ochre cube.

Finally, let the tesseract swing about the light yellow plane, so that the light green cube comes into our space, It will point downwards.

The three points, ny, m.wh, n.b, are in the cutting

Fig. 121.