Pictures in the book

All the diagrammatic pictures in this book were created using Mathematica. (The photographs were also laid out and image-processed using Mathematica.) The ability of Mathematica to manipulate graphics in a symbolic way was crucial—and was what ultimately made it possible for the book to have so many elaborate pictures.

To those familiar with book layout it may seem surprising that I was able to include so many pictures of so many different shapes and sizes without having to resort to a device like figure numbers. And indeed it required solving innumerable small geometrical puzzles to do so. But what ultimately made it possible was that the Mathematica programs for generating the pictures were almost always general enough that it was straightforward for me to get, say, a picture with a different number of cells or steps.