What is included with this book?
Preface | p. ix |
Introduction | p. 1 |
Graphs | p. 1 |
Topological notions | p. 2 |
Representation of maps | p. 9 |
Symmetry groups of maps | p. 12 |
Types of regularity of maps | p. 18 |
Operations on maps | p. 21 |
Two-faced maps | p. 24 |
The Goldberg-Coxeter construction | p. 28 |
Description of the classes | p. 31 |
Computer generation of the classes | p. 36 |
Fullerenes as tilings of surfaces | p. 38 |
Classification of finite fullerenes | p. 38 |
Toroidal and Klein bottle fullerenes | p. 39 |
Projective fullerenes | p. 41 |
Plane 3-fullerenes | p. 42 |
Polycycles | p. 43 |
(r, q)-polycycles | p. 43 |
Examples | p. 45 |
Cell-homomorphism and structure of (r, q)-polycycles | p. 48 |
Angles and curvature | p. 51 |
Polycycles on surfaces | p. 53 |
Polycycles with given boundary | p. 56 |
The problem of uniqueness of (r, q)-fillings | p. 56 |
(r, 3)-filling algorithms | p. 61 |
Symmetries of polycycles | p. 64 |
Automorphism group of (r, q)-polycycles | p. 64 |
Isohedral and isogonal (r, q)-polycycles | p. 65 |
Isohedral and isogonal (r, q)[subscript gen]-polyclcles | p. 71 |
Elementary polycycles | p. 73 |
Decomposition of polycycles | p. 73 |
Parabolic and hyperbolic elementary (R, q)[subscript gen]-polycycles | p. 76 |
Kernel-elementary polycycles | p. 79 |
Classification of elementary ({2, 3, 4, 5}, 3)[subscript gen]-polycycles | p. 89 |
Classification of elementary ({2, 3}, 4)[subscript gen]-polycycles | p. 89 |
Classification of elementary ({2, 3}, 5)[subscript gen]-polycycles | p. 90 |
Appendix 1: 204 sporadic elementary ({2, 3, 4, 5}, 3)-polycycles | p. 93 |
Appendix 2: 57 sporadic elementary ({2, 3}, 5)-polycycles | p. 102 |
Applications of elementary decompositions to (r, q)-polycycles | p. 107 |
Extremal polycycles | p. 108 |
Non-extensible polycycles | p. 116 |
2-embeddable polycycles | p. 121 |
Strictly face-regular spheres and tori | p. 125 |
Strictly face-regular spheres | p. 126 |
Non-polyhedral strictly face-regular ({a, b}, k)-spheres | p. 136 |
Strictly face-regular ({a, b}, k)-planes | p. 143 |
Parabolic weakly face-regular spheres | p. 168 |
Face-regular ({2, 6}, 3)-spheres | p. 168 |
Face-regular ({3, 6}, 3)-spheres | p. 169 |
Face-regular ({4, 6}, 3)-spheres | p. 169 |
Face-regular ({5, 6}, 3)-spheres (fullerenes) | p. 170 |
Face-regular ({3, 4}, 4)-spheres | p. 177 |
Face-regular ({2, 3}, 6)-spheres | p. 179 |
General properties of 3-valent face-regular maps | p. 181 |
General ({a, b}, 3)-maps | p. 184 |
Remaining questions | p. 186 |
Spheres and tori that are aR[subscript i] | p. 187 |
Maps aR[subscript 0] | p. 187 |
Maps 4R[subscript 1] | p. 189 |
Maps 4R[subscript 2] | p. 195 |
Maps 5R[subscript 2] | p. 203 |
Maps 5R[subscript 3] | p. 204 |
Frank-Kasper spheres and tori | p. 218 |
Euler formula for ({a, b}, 3)-maps bR[subscript 0] | p. 218 |
The major skeleton, elementary polycycles, and classification results | p. 219 |
Spheres and tori that are bR[subscript 1] | p. 225 |
Euler formula for ({a, b}, 3)-maps bR[subscript 1] | p. 225 |
Elementary polycycles | p. 229 |
Spheres and tori that are bR[subscript 2] | p. 234 |
({a, b}, 3)-maps bR[subscript 2] | p. 234 |
({5, b}, 3)-tori bR[subscript 2] | p. 237 |
({a, b}, 3)-spheres with a cycle of b-gons | p. 239 |
Spheres and tori that are bR[subscript 3] | p. 246 |
Classification of ({4, b}, 3)-maps bR[subscript 3] | p. 246 |
({5, b}, 3)-maps bR[subscript 3] | p. 252 |
Spheres and tori that are bR[subscript 4] | p. 256 |
({4, b}, 3)-maps bR[subscript 4] | p. 256 |
({5, b}, 3)-maps bR[subscript 4] | p. 270 |
Spheres and tori that are bR[subscript j] for j [greater than or equal] 5 | p. 274 |
Maps bR[subscript 5] | p. 274 |
Maps bR[subscript b] | p. 281 |
Icosahedral fulleroids | p. 284 |
Construction of I-fulleroids and infinite series | p. 285 |
Restrictions on the p-vectors | p. 288 |
From the p-vectors to the structures | p. 291 |
References | p. 295 |
Index | p. 304 |
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