Fig. 121.
The cutting space which passes through the four points, null r, y, wh, b, passes through the null r, wh, b, 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.
Fig. 122.
The three points, n.y, n.wh, n.b, are in the cutting space, and the triangle they determine is common to the tesseract and the cutting space. Hence this boundary is a triangle having a light yellow line, which is the same as the light yellow line of the first figure, a light blue line and a green line.
We have now traced the cutting space between every set of three that can be made out of the four points in which it cuts the tesseract, and have got four faces which all join on to each other by lines.