Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graphs, Skeleta and Reconstruction of Polytopes   A renowned theorem of Blind and Mani, with a constructive proof by Kalai and
an efficiency proof by Friedman, shows that the whole face lattice of a simple
polytope can be determined from its graph. This is part of a broader story of
reconstructing face lattices from partial information, first considered
comprehensively in Gr\"unbaum's 1967 book. This survey paper includes varied
results and open questions by many researchers on simplicial polytopes, nearly
simple polytopes, cubical polytopes, zonotopes, crosspolytopes, and Eulerian
posets.

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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
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The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga