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C2C2C2: Pythagorean Structures in Design
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Mark Burry, Sambit Datta, Anthony Dawson and John Rollo
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Digital Hand Eye Ear Mind: Proceedings of the Third International Conference on Mathematics and Design (M&D)
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Deakin University, Geelong, Australia
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Parametric model, Pythagorean arithmetic, Group theory, Symmetry, Configuration, Lattices, Prismatic groups, Shape studies
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The structure of the direct product group C2C2C2 is examined in detail. The foundations of the group structure in Pythagorean arithmetic are briefly presented, the realization of the group in three-dimensional space is discussed and illustrated, and some notes are suggested for its implication in music notation. A special emphasis is given in four different decompositions of the group and all subsets are enumerated and illustrated. Various applications of this structure are suggested for further systematic studies in the analysis and synthesis of the architecture of form.
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