Fig. 8.
It will be noted that in figures 8, 9 and 10, the element of perpendicularity enters as a necessary determination. In figure 8, the lines ab and bd are perpendicular to each other. Similarly, in Fig. 10, lines ab, bc, bb' and h'b are perpendicular to one another. That is, at their intersections, they make right angles. Similarly, figures representing any number of dimensions may be constructed.
Fig. 9.
Fig. 10.
The line ab represents a one-space. An entity living in a one space is called a "unodim." The plane, abcd, represents a two-space, and entities living in such a space are called duodims. The cube, abcdefgh, represents a three-space and entities inhabiting such a space are called tridims. Figure 10 represents a four-space, and its inhabitants are called quartodims. Each of the above-mentioned spaces is said to have certain limitations peculiar to itself.