  In this paper we describe the group of symmetries of a two-dimensional
continued fraction. As a multidimensional generalization of continued fractions
we consider Klein polyhedra. We distinguish two types of symmetries: the
Dirichlet-type ones, that correspond to the multiplication by units of the
corresponding number field, and so called palindromic ones. The main result of
the paper is a criterion for a two-dimensional continued fraction to have a
palindromic symmetry. This criterion is analogous to the criterion for the
period of a quadratic irrationality to be symmetric.
