Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Width Distributions for Convex Regular Polyhedra   The mean width is a measure on three-dimensional convex bodies that enjoys
equal status with volume and surface area [Rota]. As the phrase suggests, it is
the mean of a probability density f. We verify formulas for mean widths of the
regular tetrahedron and the cube. Higher-order moments of f_tetra and f_cube
have not been examined until now. Assume that each polyhedron has edges of unit
length. We deduce that the mean square width of the regular tetrahedron is
1/3+(3+sqrt(3))/(3*pi) and the mean square width of the cube is 1+4/pi.

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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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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: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: stat