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Sieve_n: A Computational Approach for the Generation of all Partial Lattices of Two-Dimensional Shapes with an n-fold Symmetry Axis
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Athanassios Economou and Thomas Grasl
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Joachim Kieferle and Karn Ehlers
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Predicting the Future: Proceedings of the Twentieth-fifth Conference of the Education and Research in Computer-Aided Architectural Design in Europe (eCAADe)
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Frankfurt am Main, Germany
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Shape studies, Generative design, Group theory, Graph theory, Shape grammars, Central buildings
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This work looks closely at a specific set of symmetry groups – the two infinite types of the planar groups, the cyclic and the dihedral ones – and pro-vides an automated environment to enumerate and represent all their subgroups and their relationships with lattices in a graph theoretic manner. The complexity of these structures can be astonishing and it is suggested here that their graph theoretical representation can contribute to a better understanding of problems of spatial complexity in architectural design. The computational approach outlined in this work can be used in formal analysis to identify all spatial repetitions and spatial correspondence observed in a design. Alternatively, the approach can be used in formal synthesis to structure the design choices and bring to the foreground the whole range of spatial relationships available to the designer at any level of the design inquiry. The paper here outlines the computational approach for the generation of all the partial order lattices of two-dimensional shapes with an n-fold symmetry axis and illustrates some of these ideas with a preliminary setting of a formal analysis of the symmetry properties of the typology of courthouses.
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