un 1 99 9 THREE , FOUR AND FIVE - DIMENSIONAL FULLERENES 1 Michel
نویسنده
چکیده
We explore some generalizations of fullerenes Fv (simple polyhedra with v vertices and only 5and -gonal faces) seen as (d−1)dimensional simple manifolds (preferably, spherical or polytopal) with only 5and 6-gonal 2-faces. First, finite and planar (infinite) 3-fullerenes are described. Three infinite families of spherical 4fullerenes are presented in Sections 4-6. The Construction A gives 4-polytopes by suitable insertion of fullerenes F30(D5h) into glued 120-cells. The Construction B gives 3-spheres by growing dodecahedra and barrels F24 around of given fullerene. The Construction C gives 4-fullerenes from special decoration of given 4-fullerene, which add facets F20, F24, F26 and F28(Td) 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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