  We develop a new purely combinatorial approach to N. Steenrod's problem on
realisation of cycles. We prove that every n-dimensional homology class of
every topological space can be realised with some multiplicity by an image of a
finite-fold covering over the manifold M^n, where M^n is the isospectral
manifold of real symmetric tridiagonal (n=1)x(n+1) matrices. In particular,
every homology class of every arcwise connected topological space can be
realised by a continuous image of an aspherical manifold.
