  For the family of multivariate probability distributions variously denoted as
unified skew-normal, closed skew-normal and other names, a number of properties
are already known, but many others are not, even some basic ones. The present
contribution aims at filling some of the missing gaps. Specifically, the
moments up to the fourth order are obtained, and from here the expressions of
the Mardia's measures of multivariate skewness and kurtosis. Other results
concern the property of log-concavity of the distribution, and closure with
respect to conditioning on intervals.
