  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.
