三维、四维和五维富勒烯
Three, four and five-dimensional fullerenes
摘要：
我们探讨了富勒烯F_v（具有v个顶点和只有5-和6-π 2-面的简单多面体）被看作只有5-和6-π 2-面的（d-1）维简单流形（最好是球形或多面体）的一些推广。首先，有限和平面（无限）3-富勒烯。在结构A、B、C中呈现了三个无限族的球形4-富勒烯。结构A通过将富勒烯F_{30}（D_{5h}）适当插入胶合的120-单元中得到4-多表位体。构造B通过在给定富勒烯周围生长十二面体和桶F_{24}而得到3-球。构造C从给定的4-富勒烯的特殊装饰得到4-富勒烯，其仅添加小面F_{20}、F_{24}、F_{26}和F_{28}（T_d）。一些5-富勒烯，通过双曲4-空间的两个规则镶嵌{5333}或其合适的替代物的粘合的变化而获得。
英文摘要：
We explore some generalizations of fullerenes F_v (simple polyhedra with v vertices and only 5- and 6-gonal faces) seen as (d-1)-dimensional simple manifolds (preferably, spherical or polytopal) with only 5- and 6-gonal 2-faces. First, finite and planar (infinite) 3-fullerenes are described. Three infinite families of spherical 4-fullerenes are presented in Constructions A,B,C. The Construction A gives 4-polytopes by suitable insertion of fullerenes F_{30}(D_{5h}) into glued 120-cells. The Construction B gives 3-spheres by growing dodecahedra and barrels F_{24} around of given fullerene. The Construction C gives 4-fullerenes from special decoration of given 4-fullerene, which add facets F_{20}, F_{24}, F_{26} and F_{28}(T_d) only. Some 5-fullerenes are obtained, by a variation of gluing of two regular tilings {5333} of hyperbolic 4-space or of their suitable quotients.
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