  The purpose of the present paper is threefold. First: giving a treatise on
weighted projective spaces by the toric point of view. Second: providing
characterizations of fans and polytopes giving weighted projective spaces, with
particular focus on a kind of \emph{recognition process} of toric data like
fans and polytopes. Third: building a mathematical framework for the
algorithmic and computational approach to wps's realized in [23,24].
