This paper presents a family of multidimensional poverty indices that measure poverty as a function of the extent and the intensity of poverty. I provide a unique axiomatics from which both extent and intensity of poverty can be derived, as well as the poor be endogenously identified. This axiomatics gives rise to a family of multidimensional indices whose extremal points are the geometric mean and the Maximin solution. I show that, in addition to all the standard features studied in the literature, these indices are continuous (a must for cardinal poverty measures) and ordinal, in the sense that they do not depend upon the units in which dimensions of achievements are computed. Moreover, they verify the decreasing rate marginal substitution property : the higher one's deprovation (or the extent of poverty) in one dimension, the smaller the increase of achievement in that dimension that suffices to compensate for a decrease of achievement in another dimension.
