Ebook: Space Structures

xiv aggregates: this touches on the very nature of things. The concept of statistical symmetry which Loeb develops is particularly important, it emphasizes the limitations in seemingly random aggregates and for permits general statements of which the crystallographer's sym­ metries are only special cases. The reductionist and holistic approaches to the world have been at war with each other since the times of the Greek philosophers and before. In nature, parts clearly do fit together into real structures, and the parts are affected by their environment. The problem is one of understanding. The mystery that remains lies largely in the nature of structural hierarchy, for the human mind can examine nature on many different scales sequentially but not simultaneously. Arthur Loeb's monograph is a fundamental one, but one can sense a devel­ opment from the relations between his zero-and three-dimensional cells to the far more complex world of organisms and concepts. It is structure that makes the difference between a cornfield and a cake, between an aggregate of cells and a human being, between a random group of human beings and a society. We can perceive anything only when we perceive its structure, and we think by structural analogy and comparison. Several books have been published showing the beauty of form in nature. This one has the beauty of a work of art, but it grows out of rigorous mathematics and from the simplest of bases-dimensional­ ity, extent and valency.

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"Space is not a passive vacuum; it has properties that constrain the patterns that exist within it." Thus does the author set the stage for a broad presentation of and informal introduction to the properties of polyhedra, such as the molecule Buckminsterfullerine. The book has a simple fundamental quality of viewpoint and treatment that gives it an unusually widespread applicability for those who share a common interest in analyzing and designing spatial structures or networks. Architects, crystallographers, artists interested in aspects of design science - as well as mathematicians, physicists, chemists, and biologists, will find here a classic and beautiful presentation of an art form, developed from rigorous mathematics and basic parameters such as dimensionality, extent, and valency. Students in all these fields, many of whom come to Professor Loeb's Department of Visual and Environmental Studies for an introduction to design science, will find the book a marvelous text.

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"Space is not a passive vacuum; it has properties that constrain the patterns that exist within it." Thus does the author set the stage for a broad presentation of and informal introduction to the properties of polyhedra, such as the molecule Buckminsterfullerine. The book has a simple fundamental quality of viewpoint and treatment that gives it an unusually widespread applicability for those who share a common interest in analyzing and designing spatial structures or networks. Architects, crystallographers, artists interested in aspects of design science - as well as mathematicians, physicists, chemists, and biologists, will find here a classic and beautiful presentation of an art form, developed from rigorous mathematics and basic parameters such as dimensionality, extent, and valency. Students in all these fields, many of whom come to Professor Loeb's Department of Visual and Environmental Studies for an introduction to design science, will find the book a marvelous text.
Content:
Front Matter....Pages i-xx
The Parameters of Structure....Pages 1-4
Valencies....Pages 5-10
The Euler-Schlaefli Equation....Pages 11-16
Statistical Symmetry....Pages 17-22
Random Two-Dimensional Nets....Pages 23-27
Degrees of Freedom....Pages 29-38
Duality....Pages 39-43
Schlegel Diagrams....Pages 45-50
Regular Structures....Pages 51-62
Truncation and Stellation....Pages 63-78
Stellation and Truncation....Pages 79-90
Exhaustive Enumeration of the Semiregular Two-dimensional Structures....Pages 91-109
Dirichlet Domains in a Plane....Pages 111-115
Dirichlet Domains of Regularly Spaced Planar Arrays....Pages 117-122
Lattices and Lattice Complexes....Pages 123-125
Space-filling Polyhedra....Pages 127-132
Additional Space Fillers and their Lattice Complexes....Pages 133-138
Orthorhombic and Tetragonal Lattices....Pages 139-146
Coda: Unwrapping the Cube: A Photographic Essay (With technical assistance of C. Todd Stuart and photography by Bruce Anderson)....Pages 147-162
Back Matter....Pages 163-188

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Content:
Front Matter....Pages i-xx
The Parameters of Structure....Pages 1-4
Valencies....Pages 5-10
The Euler-Schlaefli Equation....Pages 11-16
Statistical Symmetry....Pages 17-22
Random Two-Dimensional Nets....Pages 23-27
Degrees of Freedom....Pages 29-38
Duality....Pages 39-43
Schlegel Diagrams....Pages 45-50
Regular Structures....Pages 51-62
Truncation and Stellation....Pages 63-78
Stellation and Truncation....Pages 79-90
Exhaustive Enumeration of the Semiregular Two-dimensional Structures....Pages 91-109
Dirichlet Domains in a Plane....Pages 111-115
Dirichlet Domains of Regularly Spaced Planar Arrays....Pages 117-122
Lattices and Lattice Complexes....Pages 123-125
Space-filling Polyhedra....Pages 127-132
Additional Space Fillers and their Lattice Complexes....Pages 133-138
Orthorhombic and Tetragonal Lattices....Pages 139-146
Coda: Unwrapping the Cube: A Photographic Essay (With technical assistance of C. Todd Stuart and photography by Bruce Anderson)....Pages 147-162
Back Matter....Pages 163-188

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Content:
Front Matter....Pages i-xx
The Parameters of Structure....Pages 1-4
Valencies....Pages 5-10
The Euler-Schlaefli Equation....Pages 11-16
Statistical Symmetry....Pages 17-22
Random Two-Dimensional Nets....Pages 23-27
Degrees of Freedom....Pages 29-38
Duality....Pages 39-43
Schlegel Diagrams....Pages 45-50
Regular Structures....Pages 51-62
Truncation and Stellation....Pages 63-78
Stellation and Truncation....Pages 79-90
Exhaustive Enumeration of the Semiregular Two-dimensional Structures....Pages 91-109
Dirichlet Domains in a Plane....Pages 111-115
Dirichlet Domains of Regularly Spaced Planar Arrays....Pages 117-122
Lattices and Lattice Complexes....Pages 123-125
Space-filling Polyhedra....Pages 127-132
Additional Space Fillers and their Lattice Complexes....Pages 133-138
Orthorhombic and Tetragonal Lattices....Pages 139-146
Coda: Unwrapping the Cube: A Photographic Essay (With technical assistance of C. Todd Stuart and photography by Bruce Anderson)....Pages 147-162
Back Matter....Pages 163-188
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