Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vertex-Faithful Regular Polyhedra   We study the abstract regular polyhedra with automorphism groups that act
faithfully on their vertices, and show that each non-flat abstract regular
polyhedron covers a "vertex-faithful" polyhedron with the same number of
vertices. We then use this result and earlier work on flat polyhedra to study
abstract regular polyhedra based on the size of their vertex set. In
particular, we classify all regular polyhedra where the number of vertices is
prime or twice a prime. We also construct the smallest regular polyhedra with a
prime squared number of vertices.

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The categories of this paper are: patt-sol
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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: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th