Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-flat regular polytopes and restrictions on chiral polytopes   An abstract polytope is \emph{flat} if every facet is incident on every
vertex. In this paper, we prove that no chiral polytope has flat finite regular
facets and finite regular vertex-figures. We then determine the three smallest
non-flat regular polytopes in each rank, and use this to show that for $n \geq
8$, a chiral $n$-polytope has at least $48(n-2)(n-2)!$ flags.

10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas