Symmetry orbits
著者
書誌事項
Symmetry orbits
（Design science collection）
Birkhäuser, c1996
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注記
Includes bibliographical references (p. [233]-234)
内容説明・目次
- 巻冊次
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ISBN 9780817636616
内容説明
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.
目次
I Realization of Symmetry Groups.- 1 Groups of Isometries.- 2 Symmetry Action.- 3 Orbit Systems.- II Compounds of Cubes.- 4 Classification of the Finite Compounds of Cubes.- 5 Stability of Subcompounds.- 6 Higher Descriptives.- 7 Assembling Models.- Appendix: Historical Survey.- References.- Illustratory Contributions.
- 巻冊次
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ISBN 9783764336615
内容説明
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.
目次
- PART 1: GROUPS OF ISOMETRIES: Groups of Isometrics
- Operator Actions of Isometry Groups
- Realization Examples of Isometry Groups. PART 2: ISOMETRIC COMPOUNDS OF CUBES: Classification of the Finite Compounds of Cubes
- The Stability of Sub-Compounds
- Higher Descriptives
- Assembling Models
- Appendix: Historical Facts on Cube Compounds
- Appendix: Historical Survey
- References.
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