Fullerenes as Tilings of Surfaces
Fullerenes as Tilings of Surfaces
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DOI：
10.1021/ci990066h
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发表时间：
2000-05
期刊：
影响因子：
--
通讯作者：
M. Deza;P. Fowler;A. Rassat;K. M. Rogers
中科院分区：
文献类型：
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作者：
M. Deza;P. Fowler;A. Rassat;K. M. Rogers
如果富勒烯被定义为一个只由五边形和六边形组成的有限三价图，那么只能嵌入四个表面：球面、环面、克莱因瓶和投影（椭圆）平面。通常的球形富勒烯有12个五边形，椭圆形富勒烯有6个五边形，环形富勒烯和克莱因瓶形富勒烯没有五边形。Klein-bottle富勒烯和椭圆形富勒烯分别是中心对称的环形富勒烯和球形富勒烯的对映体。扩展到无限系统（平面富勒烯，圆柱形富勒烯，空间富勒烯）表示。本征值谱的所有四类有限富勒烯，进行了审查。蛙跳富勒烯具有相等数量的正特征值和负特征值，对于球形、椭圆形、克莱因瓶形和环形的情况，分别具有0、0、2或4个特征值零。
If a fullerene is defined as a finite trivalent graph made up solely of pentagons and hexagons, embedding in only four surfaces is possible: the sphere, torus, Klein bottle, and projective (elliptic) plane. The usual spherical fullerenes have 12 pentagons; elliptic fullerenes, 6; and toroidal and Klein-bottle fullerenes, none. Klein-bottle and elliptic fullerenes are the antipodal quotients of centrosymmetric toroidal and spherical fullerenes, respectively. Extensions to infinite systems (plane fullerenes, cylindrical fullerenes, and space fullerenes) are indicated. Eigenvalue spectra of all four classes of finite fullerenes, are reviewed. Leapfrog fullerenes have equal numbers of positive and negative eigenvalues, with 0, 0, 2, or 4 eigenvalues zero for spherical, elliptic, Klein-bottle, and toroidal cases, respectively.