Look at the views of the tesseract 1, 2, 3, or take the catalogue cubes 1, 2, 3, and place them in front of you, in any order, say running from left to right, placing 1 in the normal position, the red axis running up, the white to the right, and yellow away. Now notice that in catalogue cube 2 the colours of each region are derived from those of the corresponding region of cube 1 by the addition of blue. Thus null + blue = blue, and the corners of number 2 are blue. Again, red + blue = purple, and the vertical lines of 2 are purple. Blue + yellow = green, and the line which runs away is coloured green. By means of these observations you may be sure that catalogue cube 2 is rightly placed. Catalogue cube 3 is just like number 1. Having these cubes in what we may call their normal position, proceed to build up the three sets of blocks. This is easily done in accordance with the colour scheme on the catalogue cubes. The first block we already know. Build up the second block, beginning with a blue corner cube, placing a purple on it, and so on. Having these three blocks we have the means of representing the appearances of a group of eighty-one tesseracts. Let us consider a moment what the analogy in the case of the plane being is. He has his three sets of nine slabs each. We have our three sets of twenty-seven cubes each. Our cubes are like his slabs. As his slabs are not the things which they represent to him, so our cubes are not the things they represent to us. The plane being’s slabs are to him the faces of cubes. Our cubes then are the faces of tesseracts, the cubes by which they are in contact with our space. As each set of slabs in the case of the plane being might be considered as a sort of tray from which the solid contents of the cubes came out, so our three blocks of cubes may be considered as three-space trays, each of which is the beginning of an inch of the solid contents of the four-dimensional solids starting from them. We want now to use the names null, red, white, etc., for tesseracts. The cubes we use are only tesseract faces. Let us denote that fact by calling the cube of null colour, null face; or, shortly, null f., meaning that it is the face of a tesseract. To determine which face it is let us look at the catalogue cube 1 or the first of the views of the tesseract, which can be used instead of the models. It has three axes, red, white, yellow, in our space. Hence the cube determined by these axes is the face of the tesseract which we now have before us. It is the ochre face. It is enough, however, simply to say null f., red f. for the cubes which we use. To impress this in your mind, imagine that tesseracts do actually run from each cube. Then, when you move the cubes about, you move the tesseracts about with them. You move the face but the tesseract follows with it, as the cube follows when its face is shifted in a plane.