Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regular Polygonal Complexes in Space, II   Regular polygonal complexes in euclidean 3-space are discrete polyhedra-like
structures with finite or infinite polygons as faces and with finite graphs as
vertex-figures, such that their symmetry groups are transitive on the flags.
The present paper and its predecessor describe a complete classification of
regular polygonal complexes in 3-space. In Part I we established basic
structural results for the symmetry groups, discussed operations on their
generators, characterized the complexes with face mirrors as the 2-skeletons of
the regular 4-apeirotopes in 3-space, and fully enumerated the simply
flag-transitive complexes with mirror vector (1,2). In this paper, we complete
the enumeration of all regular polygonal complexes and in particular describe
the simply flag-transitive complexes for the remaining mirror vectors. It is
found that, up to similarity, there are precisely 25 regular polygonal
complexes which are not regular polyhedra, namely 21 simply flag-transitive
complexes and 4 complexes which are 2-skeletons of regular 4-apeirotopes.

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The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol