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Including designs by Le Corbusier, Eileen Gray, Frank Lloyd Wright, Robert Venturi, Frank Gehry, Peter Eisenman, Richard Meier and Kazuyo Sejima amongst others, this book uses mathematics to analyse arguments and theories about some of the world's most famous designs.

This book focuses on symmetries in the analysis and synthesis of architectural designs. Crucial in the history of architecture, principles of symmetry provided the means to achieve balance and harmony of spatial composition in architecture. Less well known is the importance of symmetry principles in the analysis of the distinct constituents in a contemporary architectural design which may, at first glance, appear disorganized or even random. The revelation of different hierarchical levels wherein various types of symmetry or subsymmetry are superimposed provides a key for deciphering the underlying structure of spatial logic. The interaction between local and global subsymmetries is of particular interest. Operating with symmetry concepts in this manner offers architects, designers and students an explicit method for understanding the symmetrical logics of sophisticated designs and gaining insights into new designs.This book has two complementary objectives: to explore the fundamental principles of architectural composition founded on the algebraic structure of symmetry groups in mathematics and to apply the principles in the analysis and synthesis of architectural and urban designs. By viewing and decomposing architectural and urban designs in this manner, the hidden spatial logic and underlying order in a design become transparent.

This book reviews Dante Bini¿s inventions and designs, focusing on his form-resistant Binishell and other pneumatic construction systems. Dante Bini¿s double profile of architect and builder underpins the narrative of the entire book. It is used to analyse the evolution of the early reinforced-concrete Binishell patent into a variety of automated construction systems based on the use of air. Dante Bini has always been quite proactive in promoting his work and disseminating the results of his experimentations and achievements via journal articles, conference presentations and public talks; promotional brochures in multiple languages were also prepared to export and license his patents in various countries, from Italy to the Americas and Australia. Despite this, a rigorous study of Dante Bini¿s work is still unavailable, and the relevance of this figure to contemporary architecture has yet to be discussed comprehensively. This book fills in this gap and arrives at the right time: during the last two decades, there has been an exponential interest in shell and spatial structures, particularly concerning the use of complex geometries and innovative construction techniques.This book will be of interest to academics in architectural design, theory and construction history, and practitioners and students interested in expanding their knowledge in the design and construction of shell and spatial structures.