MICHEL-MARIE DEZA is former research director at the French National Research Centre and Ecole Normale Supérieure, Paris. Earlier, he was research professor at the Japan Advanced Institute of Science and Technology. He is author of about 300 research publications on discrete geometry, combinatorics and their applications to chemistry and crystallography. He is also author of 7 books on mathematics, including popular Geometry of Cuts and Metrics and Encyclopedia of Distances, both published by Springer. MATHIEU DUTOUR SIKIRIĆ a senior associate researcher of Institute Rudjer Boskovic in Zagreb, Croatia. He is author of 70 articles and 2 books in the fields of science and engineering: mathematics, computer science, physics, chemistry, crystallography, oceanography and meteorology. His mathematical work concerns graph theory, polytope theory, tiling and their applications, geometry of numbers, and computational topology.MIKHAIL IVANOVICH SHTOGRIN is a leading research associate of Steklov Institute of Mathematics in the Russian Academy of Sciences, Moscow, Russia. He is author of over 120 research publications and 2 books on discrete geometry and geometric crystallography.

• Chapter 1. Introduction: main ZC-notions.- Chapter 2. Zigzags of fullerenes and c-disk-fullerenes.- Chapter 3. Zigzags and railroads of spheres 3_v and 4_v.- Chapter 4. ZC-circuits of 4-regular and self-dual {2,3,4}-spheres.- Chapter 5. ZC-circuits of 5- and 6-regular spheres.- Chapter 6. Goldberg–Coxeter construction and parametrization.- Chapter 7. ZC-circuits of Goldberg–Coxeter construction.- Chapter 8. Zigzags of polytopes and complexes.

MICHEL-MARIE DEZA is former research director at the French National Research Centre and Ecole Normale Supérieure, Paris. Earlier, he was research professor at the Japan Advanced Institute of Science and Technology. He is author of about 300 research publications on discrete geometry, combinatorics and their applications to chemistry and crystallography. He is also author of 7 books on mathematics, including popular Geometry of Cuts and Metrics and Encyclopedia of Distances, both published by Springer. MATHIEU DUTOUR SIKIRIĆ a senior associate researcher of Institute Rudjer Boskovic in Zagreb, Croatia. He is author of 70 articles and 2 books in the fields of science and engineering: mathematics, computer science, physics, chemistry, crystallography, oceanography and meteorology. His mathematical work concerns graph theory, polytope theory, tiling and their applications, geometry of numbers, and computational topology.MIKHAIL IVANOVICH SHTOGRIN is a leading research associate of Steklov Institute of Mathematics in the Russian Academy of Sciences, Moscow, Russia. He is author of over 120 research publications and 2 books on discrete geometry and geometric crystallography.

• Chapter 1. Introduction: main ZC-notions.- Chapter 2. Zigzags of fullerenes and c-disk-fullerenes.- Chapter 3. Zigzags and railroads of spheres 3_v and 4_v.- Chapter 4. ZC-circuits of 4-regular and self-dual {2,3,4}-spheres.- Chapter 5. ZC-circuits of 5- and 6-regular spheres.- Chapter 6. Goldberg–Coxeter construction and parametrization.- Chapter 7. ZC-circuits of Goldberg–Coxeter construction.- Chapter 8. Zigzags of polytopes and complexes.