"Here the authors give access to new results in the theory of polycycles and two-faced maps together with the relevant background material and mathematical tools for their study. Organised so that, after reading the introductory chapter, each chapter can be read independently from the others, the book should be accessible to researchers and students in graph theory, discrete geometry, and combinatorics, as well as to those in more applied areas such as mathematical chemistry and crystallography."--Jacket.
Series statement
Encyclopedia of mathematics and its applications ; v. 119
Uniform title
Encyclopedia of mathematics and its applications ; v. 119.
1. Introduction -- 2. Two-faced maps -- 3. Fullerenes as tilings of surfaces -- 4. Polycycles -- 5. Polycycles with given boundary -- 6. Symmetries of polycycles -- 7. Elementary polycycles -- 8. Applications of elementary decompositions to (r,q)-polycycles -- 9. Strictly face-regular spheres and tori -- 10. Parabolic weakly face-regular spheres -- 11. General properties of 3-valent face-regular maps -- 12. Spheres and tori that are aR[subscript i] -- 13. Frank-Kasper spheres and tori -- 14. Spheres and tori that are bR[subscript 1] -- 15. Spheres and tori that are bR[subscript 2] -- 16. Spheres and tori that are bR[subscript 3] -- 17. Spheres and tori that are bR[subscript 4] -- 18. Spheres and tori that are bR[subscript j] for j[greater than or equal to]5 -- 19. Icosahedral fulleroids.