Thus, beyond each of the eight tesseracts, which are of the same colour as the cubes which are their bases, lie eight tesseracts whose colours are derived from the colours of the first eight by adding blue. Thus—
| Null | gives | blue |
| Yellow | ” | green |
| Red | ” | purple |
| Orange | ” | brown |
| White | ” | light blue |
| Pink | ” | light purple |
| Light yellow | ” | light green |
| Ochre | ” | light brown |
The addition of blue to yellow gives green—this is a natural supposition to make. It is also natural to suppose that blue added to red makes purple. Orange and blue can be made to give a brown, by using certain shades and proportions. And ochre and blue can be made to give a light brown.
But the scheme of colours is merely used for getting a definite and realisable set of names and distinctions visible to the eye. Their naturalness is apparent to any one in the habit of using colours, and may be assumed to be justifiable, as the sole purpose is to devise a set of names which are easy to remember, and which will give us a set of colours by which diagrams may be made easy of comprehension. No scientific classification of colours has been attempted.
Starting, then, with these sixteen colour names, we have a catalogue of the sixteen tesseracts, which form a four-dimensional block analogous to the cubic block. But the cube which we can put in space and look at is not one of the constituent tesseracts; it is merely the beginning, the solid face, the side, the aspect, of a tesseract.
We will now proceed to derive a name for each region, point, edge, plane face, solid and a face of the tesseract.
The system will be clear, if we look at a representation in the plane of a tesseract with three, and one with four divisions in its side.
The tesseract made up of three tesseracts each way corresponds to the cube made up of three cubes each way, and will give us a complete nomenclature.
In this diagram, [fig. 101], 1 represents a cube of 27 cubes, each of which is the beginning of a tesseract. These cubes are represented simply by their lowest squares, the solid content must be understood. 2 represents the 27 cubes which are the beginnings of the 27 tesseracts one inch on in the fourth dimension. These tesseracts are represented as a block of cubes put side by side with the first block, but in their proper positions they could not be in space with the first set. 3 represents 27 cubes (forming a larger cube) which are the beginnings of the tesseracts, which begin two inches in the fourth direction from our space and continue another inch.
