Universidad Autonoma Metropolitana,
Keywords: nonclassical fullerenes, Euler's theorem, isolated pentagon rule
Summary:Three nonclassical fullerene are presented, they contain square and heptagonal faces, besides pentagons, and hexagons. The number of carbons are 64, 76, and 152, respectively. The first example that we consider of a nonclassical fullerene contains 64 carbons. There are 12 heptagons. The number of hexagons is 10, and finally, we have 12 squares. Each "face" of this structure is formed by 3 heptagons, next to each other, and they are surrounded by 6 hexagons, and 6 squares. In second example with 76 carbons, we have a number of pentagons equal to 24, 4 hexagons, and 12 heptagons. Therefore, it does not satisfy the so called Isolated Pentagon Rule, because there several pentagons placed together. Here, each "face" of this structure is formed by one hexagon, surrounded by 3 heptagons, and 3 pentagons. Finally, we consider a fullerene 152 carbons. In this case, each face of this structure is formed by 3 heptagons, next to each other, and they are surrounded by 6 hexagons, and 6 pentagons. Fullerenes are important on diverse applications: toxic gas sensors , fabrication of flat panel displays, and even in Art, where Vantablack, the darkest material ever made, is utilized by Anish Kapoor.