  We suggest a method to search the embeddings of Riemannian spaces with a high
enough symmetry in a flat ambient space. It is based on a procedure of
construction surfaces with a given symmetry. The method is used to classify the
embeddings of the Schwarzschild metric which have the symmetry of this
solution, and all such embeddings in a six-dimensional ambient space (i.e. a
space with a minimal possible dimension) are constructed. Four of the six
possible embeddings are already known, while the two others are new. One of the
new embeddings is asymptotically flat, while the other embeddings in a
six-dimensional ambient space do not have this property. The asymptotically
flat embedding can be of use in the analysis of the many-body problem, as well
as for the development of gravity description as a theory of a surface in a
flat ambient space.
