  The Lagrange theorem on continued fractions states that a number is a
quadratic surd if and only if its continued fraction expansion is eventually
periodic. The current paper is devoted to a multidimensional generalization of
this fact. As a multidimensional analog of continued fractions so called Klein
polyhedra are considered: given an irrational lattice in an n-dimensional
Euclidean space, its Klein polyhedron is defined as the convex hull of nonzero
lattice points with nonnegative coordinates.
