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HYPERSPHERES AND TESSERACTS 105
Figure 4.17
An 8-D cube.
We can think of these representations as "shadows" of hypercubes on 2-D
pieces of paper. Luckily, we don't have to build the object to compute what its
shadow would look like. (The computer code I used to create these forms is
listed in Appendix I.) Projections of higher-dimensional worlds have stimulated
many traditional artists to produce geometrical representations with startling
symmetries and complexities (Figs. 4.18 to 4.20).
Although computer graphic devices produce projections of higher dimensions
on mere 2-D screens, the computer can store the location of points in higher
dimensions for manipulations such as rotation and magnification. The computer
can then display projections of these higher-dimensional forms from various
viewpoints. In fact, the computer is frequently used to represent higher dimen-