Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compact hyperbolic Coxeter $4$-polytopes with $8$ facets   Unlike the spherical and parabolic cases, complete classification regarding
hyperbolic Coxeter polytopes of finite volume is far from being obtained.
Poincar\'{e} and Andreev addressed this problems in dimensions $2$ and $3$,
respectively. In dimensions larger than or equal to four, complete
classifications of Coxeter polytopes are achieved scatteredly only in the cases
of simplexes, $n$-polytopes of finite volume with $n+2$ facets and bounded
$n$-polytope with $n+3$ facets, etc. We obtain the complete classification for
compact hyperbolic Coxeter $4$-polytopes with $8$ facets.

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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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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: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio