Forward Preface Part I. Incidence: Introduction Section 1. Incidence and Graph Theory: 1. Topological transformations 2. Basic graph theory 3. Directed graphs 4. Traversability 5. Distance Section II. Incidence in the Plane: 6. Maps 7. Planar graphs 8. Euler's formula 9. Polyhedra Section III. Further Applications of Graph Theory: 10. Bracing structures 11. Optimal route design 12. Mean distance 13. Triangulations and organization graphs Section IV. Topology of Surfaces: 14. Surfaces 15. Maps on surfaces 16. Tesselations of the plane 17. Compact surfaces Part II. Symmetry: Introduction Section V. Symmetry and Group Theory: 18. Planar isometries 19. Basic group theory 20. Reflections on the plane 21. The isometry group of the plane Section VI. Symmetry in the Plane: 22. Discrete groups 23. The circular groups 24. The frieze groups 25. The wallpaper groups Section VII. Symmetry in Space: 26. Space isometries 27. Discrete space groups 28. The layer groups 29. the rod groups Section VIII. Symmetry and Enumeration: 30. A combinational approach to symmetry 31. Graph symmetry 32. Enumeration 33. Fundamental architectural arrangements revisited Bibliography Indices.
Forward Preface Part I. Incidence: Introduction Section 1. Incidence and Graph Theory: 1. Topological transformations 2. Basic graph theory 3. Directed graphs 4. Traversability 5. Distance Section II. Incidence in the Plane: 6. Maps 7. Planar graphs 8. Euler's formula 9. Polyhedra Section III. Further Applications of Graph Theory: 10. Bracing structures 11. Optimal route design 12. Mean distance 13. Triangulations and organization graphs Section IV. Topology of Surfaces: 14. Surfaces 15. Maps on surfaces 16. Tesselations of the plane 17. Compact surfaces Part II. Symmetry: Introduction Section V. Symmetry and Group Theory: 18. Planar isometries 19. Basic group theory 20. Reflections on the plane 21. The isometry group of the plane Section VI. Symmetry in the Plane: 22. Discrete groups 23. The circular groups 24. The frieze groups 25. The wallpaper groups Section VII. Symmetry in Space: 26. Space isometries 27. Discrete space groups 28. The layer groups 29. the rod groups Section VIII. Symmetry and Enumeration: 30. A combinational approach to symmetry 31. Graph symmetry 32. Enumeration 33. Fundamental architectural arrangements revisited Bibliography Indices.
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