  Being motivated by the theory of flexible polyhedra, we study the Dirichlet
and Neumann eigenvalues for the Laplace operator in special bounded domains of
Euclidean $d$-space. The boundary of such a domain is an embedded simplicial
complex which allows a continuous deformation (a flex), under which each
simplex of the complex moves as a solid body and the change in the spatial
shape of the domain is achieved through a change of the dihedral angles only.
The main result of this article is that both the Dirichlet and Neumann spectra
of the Laplace operator in such a domain do not necessarily remain unaltered
during the flex of its boundary.
