The homology and cohomology of the complements to some arrangements of codimension two complex planes

We consider the homology and cohomology of the complement to the arrangement $Z=\bigcup_{1<|i-j|<d-1}\{z_i=z_j=0\}$ of coordinate planes in $\mathbb C^d$, and explicitly construct a basis for these groups as well as a basis for the homology groups of the one-point compactification of $Z$.