Ebook: Symmetry Orbits

In a broad sense design science is the grammar of a language of images rather than of words. Modem communication techniques enable us to transmit and reconstitute images without needing to know a specific verbal sequence language such as the Morse code or Hungarian. Inter­ national traffic signs use international image symbols which are not An image language differs specific to any particular verbal language. from a verbal one in that the latter uses a linear string of symbols, whereas the former is multidimensional. Architectural renderings commonly show projections onto three mutually perpendicular planes, or consist of cross sections at different altitudes capable of being stacked and representing different floor plans. Such renderings make it difficult to imagine buildings compris­ ing ramps and other features which disguise the separation between and consequently limit the creative process of the architect. floors, Analogously, we tend to analyze natural structures as if nature had used similar stacked renderings, rather than, for instance, a system of packed spheres, with the result that we fail to perceive the system of organization determining the form of such structures.

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Symmetry groups are of intense interest to mathematicians, physicists, chemists, and designers, as well as to the "philomorphs" who are attracted to the ideas of Design Science. The author of this book has beautifully illustrated active symmetry through the observation of the orbit of a plain cube as it creates an arrangement of cube replicas with overall symmetry under such a specific group. For the general reader, the beauty and utility of the resulting pictures is evident. The mathematician, scientific investigator or student will further welcome a full description of all finite symmetry groups with relevant drawings, calculations, and data. In the detailed study of the cube's orbits, a complete enumeration of cube compounds is introduced and illustrated by photographs, patterns, and constructable models. This group theoretical approach demonstrates a step forward in the long attempt at full classification of polyhedral compounds, whose history is treated in a special chapter in the book. The method includes construction of single polyhedra and allows a logical creation of their compounds never before published. A more complete understanding of symmetry is thus granted. The book will appeal to a wide range of researchers and students, even at the undergraduate level, in geometry, crystallography, structural chemistry, engineering, architecture and the developing discipline of Design Science.

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Symmetry groups are of intense interest to mathematicians, physicists, chemists, and designers, as well as to the "philomorphs" who are attracted to the ideas of Design Science. The author of this book has beautifully illustrated active symmetry through the observation of the orbit of a plain cube as it creates an arrangement of cube replicas with overall symmetry under such a specific group. For the general reader, the beauty and utility of the resulting pictures is evident. The mathematician, scientific investigator or student will further welcome a full description of all finite symmetry groups with relevant drawings, calculations, and data. In the detailed study of the cube's orbits, a complete enumeration of cube compounds is introduced and illustrated by photographs, patterns, and constructable models. This group theoretical approach demonstrates a step forward in the long attempt at full classification of polyhedral compounds, whose history is treated in a special chapter in the book. The method includes construction of single polyhedra and allows a logical creation of their compounds never before published. A more complete understanding of symmetry is thus granted. The book will appeal to a wide range of researchers and students, even at the undergraduate level, in geometry, crystallography, structural chemistry, engineering, architecture and the developing discipline of Design Science.
Content:
Front Matter....Pages i-vii
Introduction....Pages 1-8
Front Matter....Pages 9-9
Groups of Isometries....Pages 11-66
Symmetry Action....Pages 67-79
Orbit Systems....Pages 81-91
Front Matter....Pages 93-93
Classification of the Finite Compounds of Cubes....Pages 95-159
Stability of Subcompounds....Pages 161-194
Higher Descriptives....Pages 195-200
Assembling Models....Pages 201-221
Back Matter....Pages 223-236

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Content:
Front Matter....Pages i-vii
Introduction....Pages 1-8
Front Matter....Pages 9-9
Groups of Isometries....Pages 11-66
Symmetry Action....Pages 67-79
Orbit Systems....Pages 81-91
Front Matter....Pages 93-93
Classification of the Finite Compounds of Cubes....Pages 95-159
Stability of Subcompounds....Pages 161-194
Higher Descriptives....Pages 195-200
Assembling Models....Pages 201-221
Back Matter....Pages 223-236

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Content:
Front Matter....Pages i-vii
Introduction....Pages 1-8
Front Matter....Pages 9-9
Groups of Isometries....Pages 11-66
Symmetry Action....Pages 67-79
Orbit Systems....Pages 81-91
Front Matter....Pages 93-93
Classification of the Finite Compounds of Cubes....Pages 95-159
Stability of Subcompounds....Pages 161-194
Higher Descriptives....Pages 195-200
Assembling Models....Pages 201-221
Back Matter....Pages 223-236
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