Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrable lattices of hyperplanes related to billiards within confocal
  quadrics   We introduce a new discrete system that arises from ellipsoidal billiards and
is closely related to the double reflection nets. The system is defined on the
lattice of a uniform honeycomb consisting of rectified hypercubes and cross
polytopes. In the $2$-dimensional case, the lattice is regular and it
incorporates dynamics both in the original space and its dual. In the
$3$-dimensional case, the lattice consists of tetrahedra and cuboctahedra.

7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc