  In this paper we study the topological structure of moment-angle complexes
$\mathcal{Z_K}$. We consider two classes of simplicial complexes. The first
class $B_{\Delta}$ consists of simplicial complexes $\mathcal{K}$ for which
$\mathcal{Z_K}$ is homotopy equivalent to a wedge spheres. The second class
$W_{\Delta}$ consists of $\mathcal{K}\in B_{\Delta}$ such that all spheres in
the wedge are realized by iterated higher Whitehead products. Buchstaber and
Panov asked if it is true that $B_{\Delta} = W_{\Delta}$. In this paper we show
that this is not the case. Namely, we give an example of a simplicial complex
whose corresponding moment-angle complex is homotopy equivalent to a wedge of
spheres, but there is a sphere which cannot be realized by any linear
combination of iterated higher Whitehead products.
  On the other hand we show that class $W_{\Delta}$ is large enough. Namely, we
show that the class $W_{\Delta}$ is closed with respect to two explicitly
defined operations on simplicial complexes. Then using these operations we
prove that there exists a simplicial complex that realizes any given iterated
higher Whitehead product. Also we describe the smallest simplicial complex that
realizes an iterated product with only two pairs of nested brackets.
