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instructions for the construction of an enormous number or new and fascinating mathematical models of interest to students of euclidean geometry and topology, both secondary and collegiate, to designers, engineers and architects, to the scientific audience concerned with molecular and other structural problems, and to mathematicians, both professional and dilettante, with hundreds of exercises and search projects, many outlined for self-instruction".
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The second edition describes its intended audience in an elaborate subtitle, a throwback to times when long subtitles were more common: "a study of Quasi-Convex, aplanar, tunneled orientable polyhedra of positive genus having regular faces with disjoint interiors, being an elaborate description and
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in landscape mode compared to the tall and narrow 5 inches (13 cm) by 13 inches (33 cm) page size of the first edition, with two columns per page. It includes new material on knotted polyhedra and on rings of regular octahedra and regular dodecahedra; as the ring of dodecahedra forms the
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than the sphere. Many of these polyhedra can be formed by gluing together smaller polyhedral pieces, carving polyhedral tunnels through them, or piling them into elaborate towers. The toroidal polyhedra described in this book, formed from regular polygons with no self-intersections or flat angles,
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Mathematician Joseph A. Troccolo calls a method of constructing physical models of polyhedra developed in the book, using cardboard and rubber bands, "of inestimable value in the classroom". One virtue of this technique is that it allows for the quick disassembly and reuse of its parts.
108:, known to antiquity, have all faces regular polygons, all symmetric to each other (each face can be taken to each other face by a symmetry of the polyhedron). However, if less symmetry is required, a greater number of polyhedra can be formed while having all faces regular. The
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extends the investigation of polyhedra with regular faces to non-convex polyhedra, and in particular to polyhedra of higher
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summarizes the book as "a remarkable combination of sound mathematics, art, instruction and humor", while
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calls it "highly recommended" to others interested in polyhedra and their juxtapositions.
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Adventures Among the
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as their faces. It was written, hand-lettered, and illustrated by mathematician
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Adventures Among the
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Troccolo, Joseph A. (March 1976), "The algebra and geometry of polyhedra",
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has recommended its inclusion in undergraduate mathematics libraries.
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One of the
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Prichett, Gordon D. (January 1976), "Three-dimensional discovery",
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A ring of octahedra discussed in the second edition of the book
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The second edition is rewritten in a different page format,
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and A. P. Rollett), and have come to be known as the
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195:Henry Crapo
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351:(2nd ed.)"
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