In this paper we study a new combinatorial invariant of simple polytopes,
which comes from toric topology. With each simple n-polytope P with m facets we
can associate a moment-angle complex Z_P with a canonical action of the torus
T^m. Then s(P) is the maximal dimension of a toric subgroup that acts freely on
Z_P. The problem stated by Victor M. Buchstaber is to find a simple
combinatorial description of an s-number. We describe the main properties of
s(P) and study the properties of simple n-polytopes with n+3 facets. In
particular, we find the value of an s-number for such polytopes, a simple
formula for their h-polynomials and the bigraded cohomology rings of the
corresponding moment-angle complexes