The fourth dimension

142 THE FOURTH DIMENSION

thus formed would have red, white, and yellow lines surrounding pink, orange, and light yellow faces. The ochre cubes increase in three ways, and hence ultimately the whole interior of the cube would be coloured ochre.

We have thus a nomenclature for the points, lines, faces, and solid content of a cube, and it can be named as exhibited in fig. 85.

We can consider the cube to be produced in the following way. A null point moves in a direction to which we attach the colour indication yellow; it generates a yellow line and ends in a null point. The yellow line thus generated moves in a direction to which we give the colour indication red. This lies up in the figure. The yellow line traces out a yellow, red, or orange square, and each of its null points trace out a red line, and ends in a null point.

This orange square moves in a direction to which we attribute the colour indication white, in this case the direction is the right. The square traces ont a cube coloured orange, red, or ochre, the red lines trace out red to white or pink squares, and the yellow lines trace out light yellow squares, each line ending in a line of its own colour. While the points each trace out a null + white, or white line to end in a null point.

Now returning to the first block of eight cubes we can name each point, line, and square in them by reference to the colour scheme, which they determine by their relation to each other.

Thus, in fig. 86, the null cube touches the red cube by

i :