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Being motivated by the theory of flexible polyhedra, we study the Dirichletand Neumann eigenvalues for the Laplace operator in special bounded domains ofEuclidean $d$-space. The boundary of such a domain is an embedded simplicialcomplex which allows a continuous deformation (a flex), under which eachsimplex of the complex moves as a solid body and the change in the spatialshape 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 spectraof the Laplace operator in such a domain do not necessarily remain unalteredduring the flex of its boundary.

The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in $\mathbb R^d$ does not always remain unaltered during the flex