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The mathematician and mechanical engineer authors of this volume further strengthen the link between origami and mathematics – and expand the relationship to crystallography. Through a series of photographs, diagrams, and charts, they illustrate the correlation between the origami waterbomb base and the mathematical duality principle of Archimedean solids. Then, they show how to apply the correlation to models of the buckyball (a carbon-60 molecule resembling a soccer ball, named for R. Buckminster Fuller, designer of the geodesic dome). By the process of gyroscope transformation, origamists can transform buckyballs into more new and interesting shapes. Step-by-step instructions and clear diagrams show origami enthusiasts how to create a world of multifaceted wonders.