The points are common to six square faces and to four cubes; thus, the null point from which we start is common to the three square faces—pink, light yellow, orange, and to the three square faces made by moving the three lines white, yellow, red, in the fourth dimension, namely, the light blue, the light green, the purple faces—that is, to six faces in all. The four cubes which meet in it are the ochre cube, the light purple cube, the brown cube, and the light green cube. [Illustration: Fig. 103. The tesseract, red, white, yellow axes in space. In the lower line the three rear faces are shown, the interior being removed.] [Illustration: Fig. 104. The tesseract, red, yellow, blue axes in space, the blue axis running to the left, opposite faces are coloured identically.] A complete view of the tesseract in its various space presentations is given in the following figures or catalogue cubes, figs. 103-106. The first cube in each figure represents the view of a tesseract coloured as described as it begins to pass transverse to our space. The intermediate figure represents a sectional view when it is partly through, and the final figure represents the far end as it is just passing out. These figures will be explained in detail in the next chapter. [Illustration: Fig. 105. The tesseract, with red, white, blue axes in space. Opposite faces are coloured identically.] [Illustration: Fig. 106. The tesseract, with blue, white, yellow axes in space. The blue axis runs downward from the base of the ochre cube as it stands originally. Opposite faces are coloured identically.] We have thus obtained a nomenclature for each of the regions of a tesseract; we can speak of any one of the eight bounding cubes, the twenty square faces, the thirty-two lines, the sixteen points. CHAPTER XIII REMARKS ON THE FIGURES