Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous deformations of polyhedra that do not alter the dihedral
  angles   We prove that, both in the hyperbolic and spherical 3-spaces, there exist
nonconvex compact boundary-free polyhedral surfaces without selfintersections
which admit nontrivial continuous deformations preserving all dihedral angles
and study properties of such polyhedral surfaces. In particular, we prove that
the volume of the domain, bounded by such a polyhedral surface, is necessarily
constant during such a deformation while, for some families of polyhedral
surfaces, the surface area, the total mean curvature, and the Gauss curvature
of some vertices are nonconstant during deformations that preserve the dihedral
angles. Moreover, we prove that, in the both spaces, there exist tilings that
possess nontrivial deformations preserving the dihedral angles of every tile in
the course of deformation.

14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc