The fourth dimension

REMARKS ON THE FIGURES 195

face in an orange line with null points, This then is one of the boundaries of the section figure.

Let now the cube be so turned that the pink face comes in his plane. The points null r and null wh are now visible The line between them is pink with null points, and since this line is common to the surface of the cube and the cutting plane, it is a boundary of the figure in which the plane cuts the cube.

Again, suppose the cube turned so that the light yellow face is in contact with the plane being’s plane. He sees two points, the null wh and the null y. The line between these lies in the cutting plane. Hence, since the three cutting lines meet and enclose a portion of the cube between them, he has determined the figure he sought. It is a triangle with orange, pink, and light yellow sides, all equal, and enclosing an ochre area.

Let us now determine in what figure the space, determined by the four points, null 7, null y, null wh, null b, cuts the tesseract. We can see three of these points in the primary position of the tesseract resting against our solid sheet by the ochre cube. These three points determine a plane which lies in the space we are considering, and this plane cuts the ochre cube in a triangle, the interior of which is ochre (fig. 119 will serve for this view), with pink, light yellow and orange sides, and null points. Going in the fourth direction, in one sense, from this plane we pass into the tesseract, in the other sense we pass away from it. The whole area inside the triangle is common to the cutting plane we see, and a boundary of the tesseract. Hence we conclude that the triangle drawn is common to the tesseract and the cutting space,