This study explores the concentration indexes, such as the Gini, the Theil and the Atkinson indexes, from the geometric perspective. The algebraic formulations of these indexes are reinterpreted within the framework of the n-dimensional simplex, a geometric representation of resource distributions. By mapping the phenomenon under investigation throughout the position of points within the simplex, the study highlights the intrinsic relationships between wealth inequality and geometric principles. Furthermore, the research introduces new indexes grounded in the geometry of the simplex, providing innovative tools for quantifying wealth distribution. These indexes leverage distance-based metrics of the simplex, offering a fresh approach to inequality measurement. The proposed methodology enriches the analysis of wealth inequality by bridging algebraic and geometric paradigms, offering deeper insights into the structural underpinnings of inequality. These findings have potential implications for both theoretical research and practical applications in economic inequality studies.