Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of spherical tilings by congruent quadrangles over
  pseudo-double wheels (I) -- a special tiling by congruent concave quadrangles   Every simple quadrangulation of the sphere is generated by a graph called a
pseudo-double wheel with two local expansions (Brinkmann et al. "Generation of
simple quadrangulations of the sphere." Discrete Math., Vol. 305, No. 1-3, pp.
33-54, 2005). So, toward classification of the spherical tilings by congruent
quadrangles, we propose to classify those with the tiles being convex and the
graphs being pseudo-double wheels. In this paper, we verify that a certain
series of assignments of edge-lengths to pseudo-double wheels does not admit a
tiling by congruent convex quadrangles. Actually, we prove the series admits
only one tiling by twelve congruent concave quadrangles such that the symmetry
of the tiling has only three perpendicular 2-fold rotation axes, and the tiling
seems new.

28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ