Given a table $T$ with $D$ dimensions, the skycube of $T$ is the union of all skylines obtained by considering each of the subsets of $D$ (subspaces). The number of these skylines is exponential w.r.t $D$. To make the skycube practically useful, two lines of research have been pursued so far: the first one aims to propose efficient algorithms for computing it and the second one considers either that the skycube is too large to be computed in a reasonable time or it requires too much memory space to be stored. They therefore propose skycube summarization techniques to reduce time and space consumption. Intuitively, previous efforts have been devoted to compute or summarize the following information: "for every tuple $t$, list the skylines where $t$ belongs to". In this paper, we consider the complementary statement, i.e., "for every tuple $t$, list the skylines where $t$ {\em does not belong to}". This is what we call the {\em negative skycube}. Despite the apparent equivalence between these two statements, our analysis and extensive experiments show that these two points of views do not lead to the same behavior of the related algorithms. More specifically, our proposal shows that (i) the negative summary can be obtained much faster than state of the art techniques for positive summaries, (ii) in general, it consumes less space, (iii) skyline queries evaluation using this summary are much faster, (iv) the positive skycube can be obtained much more rapidly than state of the art algorithms, and (v) it can be used for a larger class of queries, namely $k$-domination skylines.