SOME ASPECTS OF THE SYMMETRY AND TOPOLOGY OF POSSIBLE CARBON ALLOTROPE STRUCTURES

摘要: Elemental carbon has recently been shown to form molecular polyhedral allotropes known as fullerenes in addition the familiar graphite and diamond since antiquity. Such contain cages which all vertices have degree 3 faces are either pentagons or hexagons. All found satisfy isolated pentagon rule (IPR) pentagonal completely surrounded by hexagons so that no two share an edge. The smallest fullerene structures satisfying IPR truncated icosahedral C60 of I h symmetry ellipsoidal C70 D 5h symmetry. multiple isomers families larger such C76, C78, C82 C84 can be classified into related so-called pyracylene transformation based on motion atoms a unit containing linked separated Larger with 3ν generated from smaller ν through so‐called leapfrog consisting omnicapping followed dualization. energy levels bonding orbitals having 60n 2 approximated spherical harmonics. If regarded constructed networks positive curvature, corresponding negative curvature polymeric schwarzites. schwarzites is introduced heptagons octagons placing minimal surfaces Gaussian particularly P local cubic cell viable schwarzite structure only contains 168 applying genus figure 24 56 described German mathematician Klein 19th century analogous construction icosahedron regular dodecahedron. Although this C168 O point group lattice surface, its permutational PSL(2,7) order pure rotation group, I, 60 considered isomorphous PSL(2,5) group. schwarzites, still unknown experimentally, predicted unusually low density forms elemental because pores infinite periodicity three dimensions underlying surfaces.