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Regular figures /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
[Place of publication not identified] :
Pergamon Press,
1964.
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| Colección: | International series in pure and applied mathematics ;
48. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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 FIGURES30. The isoperimetric property of the regular spherical polygons; 31. Shortest spherical net with meshes of equalarea; 32. An extremal distribution of great circles; 33. An inequality for star-tessellations; 34. A covering problem; 35. Distribution of the orifices on pollen-grains; 36. Remarks; CHAPTERVIII. PROBLEMS IN THE HYPERBOLIC PLANE; 37. Circle-packings and circle-coverings; 38. Packing and covering by horocycles; 39. An extremum property of the tessellations {p, 3}; 40. Remarks; CHAPTERIX. PROBLEMS IN 3-SPACE; 41. Volume estimates for polyhedra
- 42. Surface area and edge-curvature43. The isoperimetric problem for polyhedra; 44. Sphere-clouds; 45. Sphere-packings and sphere-coverings; 46. Honeycombs; 47. Remarks; CHAPTERX. PROBLEMS IN HIGHER SPACES; 48. On the volume of a polyhedron in non-Euclidean 3-space; 49. Extremum properties of the regular polytopes; 50. Sphere-packings and sphere-coverings in spaces of constant curvature; 51. Remarks; Postscript; Bibliography; Index