Fivefold Symmetry

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Fivefold symmetry is common in flowers, fruits, molecules, logos, and buildings, but it is a forbidden symmetry in the world of crystals. A few years ago, the so-called quasicrystals were discovered displaying fivefold symmetry, and it caused a minirevolution in crystallography. There has been increased awareness of fivefold symmetry in all domains of human interest ever since. The present book brings together authors and ideas on a common theme from mathematics, the sciences, design, and anthropology to history, literature, and the arts. Its 29 chapters are an offering by scientists and humanists from 13 countries to a broad readership of professionals and laypersons about fivefold symmetry and the areas that are being bridged by this unique concept.
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Editorial Reviews

The diversity of topics addressed in 29 contributions makes for a vibrant inquiry into one particular symmetry. Among the topics: Hawaiian flowers, the graphic art of M.C. Escher, early Hindu thought, basket weaving in various cultures, and Egyptian and Christian iconography, as well as plane projections of regular polytopes, continuous transformations of non-periodic tilings, hyperbolic crystallography, and the pentasnow gasket and its fractal dimension. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9789810206000
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 3/28/1992
  • Pages: 580
  • Product dimensions: 6.31 (w) x 8.79 (h) x 1.16 (d)

Table of Contents

Fivefold Symmetry: A Lesser Symmetry 1
Fivefold Symmetry in Mathematics, Physics, Chemistry, Biology, and Beyond 11
The Relationship Between Mathematics and Mysticism of the Golden Mean Through History 33
800-Year-Old Pentagonal Tiling From Maragha, Iran, and the New Varieties of Aperiodic Tiling it Inspired 67
Plane Projections of Regular Polytopes with Fivefold Symmetries 87
Continuous Transformations of Non-Periodic Tilings and Space-Fillings 97
Fivefold Symmetry in Hyperbolic Crystallography 129
The Pentasnow Gasket and its Fractal Dimension 141
Pentagonal Chaos 151
How to Inscribe a Dodecahedron in a Sphere 167
Complete Symmetry of Figures with Fivefold Symmetry Axes 171
Icosahedral Morphology 177
The Discovery of Space Frames with Fivefold Symmetry 205
The New Zome Primer 221
A Unique Fivefold Symmetrical Building: A Calvinist Church in Szeged, Hungary 235
Fivefold Symmetry and (Basket) Weaving in Various Cultures 245
Pentagon and Decagon Designs in Islamic Art 263
An Islamic Pentagonal Seal (from Scientific Manuscripts of the Geometry of Design) 283
Notes on Some Pentagonal "Mysteries" in Egyptian and Christian Iconography 307
The Icosahedral Design of the Great Pyramid 333
A Mystic History of Fivefold Symmetry in Japan 361
Fivefold Symmetry in the Literature 395
The Allegorical Method and Systems of Fives--A Beginning Discussion Exemplified in Beowulf 407
Certain Quinary Aspects of the Hindu Civilization 423
On the Shape of Five in Early Hindu Thought 445
Albrecht Durer and the Regular Pentagon 465
Fivefold Symmetry in the Graphic Art of M.C. Escher 489
Nomothetical Modelling of Spiral Symmetry in Biology 505
Hawaiian Flowers with Fivefold Symmetry 529
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