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The first chapter discusses regular polygons, regular polyhedra, basic concepts of Graph theory, and the Euler characteristic. Using the Euler characteristic, Coxeter derives a Diophantine equation whose integer solutions describe and classify the regular polyhedra. The second chapter uses combinations of regular polyhedra and their duals to generate related polyhedra, including the semiregular polyhedra, and discusses zonohedra and Petrie polygons. Here and throughout the book, the shapes it discusses are identified and classified by their Schläfli symbols.