Regular figures

by Fejes Tóth, L.

Type Book
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Regular Figures concerns the systematology and genetics of regular figures. The first part of the book deals with the classical theory of the regular figures. This topic includes description of plane ornaments, spherical arrangements, hyperbolic tessellations, polyhedral, and regular polytopes. The problem of geometry of the sphere and the two-dimensional hyperbolic space are considered. Classical theory is explained as describing all possible symmetrical groupings in different spaces of consta…

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Title Statements

  • Full title :Regular figures / L. Fejes Tóth.

Summary

Regular Figures concerns the systematology and genetics of regular figures. The first part of the book deals with the classical theory of the regular figures. This topic includes description of plane ornaments, spherical arrangements, hyperbolic tessellations, polyhedral, and regular polytopes. The problem of geometry of the sphere and the two-dimensional hyperbolic space are considered. Classical theory is explained as describing all possible symmetrical groupings in different spaces of constant curvature. The second part deals with the genetics of the regular figures and the inequalities fo.

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Edition Statements

  • Publication Date:1964.

Publication Statements

  • Publisher(s):Pergamon Press
  • Place of Publication:Place of publication not identified
  • Language:eng
  • Publication Date:1964.

The Physical Object

  • Description:1 online resource : : illustrations

Edition Identifiers

  • oclc:ocn896412951
  • LC Classification:QA174.7.S96
  • Dewey Decimal:516/.1

Table of Contents

Front Cover; Regular Figures; Copyright Page; Table of Contents; Preface; PART ONE: SYSTEMATOLOGY OF THE REGULAR FIGURES; CHAPTER I. PLANE ORNAMENTS; 1. Isometries; 2. Symmetry groups; 3. Groups with infinite unit cells; 4. Groups with finite unit cells; 5. Remarks; CHAPTERII. SPHERICAL ARRANGEMENTS; 6. Isometries in space; 7. The finite rotation groups; 8. The finite symmetry groups; 9. Groups of permutations; 10. The geometrical crystal classes; 11. Remarks; CHAPTERIII. HYPERBOLIC TESSELLATIONS; 12. The hyperbolic plane; 13. Hyperbolic trigonometry; 14. Hyperbolic tessellations; 15. Remarks

CHAPTERIV. POLYHEDRA16. The nine regular polyhedra; 17. Semi-regular polyhedra; 18. Parallelohedra; 19. Remarks; CHAPTERV. REGULAR POLYTOPES; 20. Geometry in more than three dimensions; 21. The general regular polytope; 22. The convex regular polytopes; 23. Remarks; PART TWO: GENETICS OF THE REGULAR FIGURES; CHAPTERVI. FIGURES IN THE EUCLIDEAN PLANE; 24. Inequalities for polygons; 25. Packing and covering problems; 26. Isoperimetric problems in cell-aggregates; 27. Packings and coverings by non-congruent circles; 28. A stability problem for circle-packings; 29. Remarks

CHAPTERVII. SPHERICAL…

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Subjects

Decoration and ornament Décoration et ornement symétrie symmetry Topologie Topology Transformations (Mathematics)

Writers

Fejes Tóth, L.

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