Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal ball and horoball packings generated by $3$-dimensional simply
  truncated Coxeter orthoschemes with parallel faces   In this paper we consider the ball and horoball packings belonging to
$3$-dimensional Coxeter tilings that are derived by simply truncated
orthoschemes with parallel faces.
  The goal of this paper to determine the optimal ball and horoball packing
arrangements and their densities for all above Coxeter tilings in hyperbolic
3-space $\mathbb{H}^3$. The centers of horoballs are required to lie at ideal
vertices of the polyhedral cells constituting the tiling, and we allow
horoballs of different types at the various vertices.
  We prove that the densest packing of the above cases is realized by horoballs
related to $\{\infty;3;6;\infty \}$ and $\{\infty;6;3;\infty \}$ tilings with
density $\approx 0.8413392$.

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The categories of this paper are: nucl-th
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The categories of this paper are: cs
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex