Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three, four and five-dimensional fullerenes   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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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: stat
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph