Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Wythoffian Skeletal Polyhedra in Ordinary Space, I   Skeletal polyhedra are discrete structures made up of finite, flat or skew,
or infinite, helical or zigzag, polygons as faces, with two faces on each edge
and a circular vertex-figure at each vertex. When a variant of Wythoff's
construction is applied to the forty-eight regular skeletal polyhedra
(Grunbaum-Dress polyhedra) in ordinary space, new highly symmetric skeletal
polyhedra arise as "truncations" of the original polyhedra. These Wythoffians
are vertex-transitive and often feature vertex configurations with an
attractive mix of different face shapes. The present paper describes the
blueprint for the construction and treats the Wythoffians for distinguished
classes of regular polyhedra. The Wythoffians for the remaining classes of
regular polyhedra will be discussed in Part II, by the second author. We also
examine when the construction produces uniform skeletal polyhedra.

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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph