  In various approaches, data cubes are pre-computed in order to answer
efficiently OLAP queries. The notion of data cube has been declined in various
ways: iceberg cubes, range cubes or differential cubes. In this paper, we
introduce the concept of convex cube which captures all the tuples of a
datacube satisfying a constraint combination. It can be represented in a very
compact way in order to optimize both computation time and required storage
space. The convex cube is not an additional structure appended to the list of
cube variants but we propose it as a unifying structure that we use to
characterize, in a simple, sound and homogeneous way, the other quoted types of
cubes. Finally, we introduce the concept of emerging cube which captures the
significant trend inversions. characterizations.
