  We show how a $d$-stress on a piecewise-linear realization of an oriented
(non-simplicial, in general) $d$-manifold in \rd naturally induces stresses of
lower dimensions on this manifold, and discuss implications of this
construction to the analysis of self-stresses in spatial frameworks. The
constructed mappings are not linear, but polynomial. In 1860-70s J. C. Maxwell
described an interesting relationship between self-stresses in planar
frameworks and vertical projections of polyhedral 2-surfaces. We offer a
partial analog of Maxwell correspondence for self-stresses in spatial
frameworks and vertical projections of 3-dimensional surfaces based on our
construction of polynomial mappings. Applying this theorem we derive a class of
three-dimensional spider webs similar to the family of two-dimensional spider
webs described by Maxwell. In addition, we conjecture an important property of
our mappings which is supported by a heuristic count based on the lower bound
theorem ($g_2(d+1)=dim\:Stress_2 \ge 0$) for $d$-pseudomanifolds generically
realized in ${\R}^{d+1}$ (Fogelsanger).
