The problem of defining a support for multidimensional range queries on P2P overlays is currently an active field of research. Several approaches based on the extension of the basic functionalities offered by Distributed Hash Tables have been recently proposed. The main drawback of these approaches is that the locality required for the resolution of a range query cannot be guaranteed by uniform hashing. On the other way, locality preserving hashing functions do not guarantee a good level of load balancing. This paper presents Hivory, a P2P overlay based on a Voronoi tessellation defined by the objects published by peers. Each object is mapped to a site of the Voronoi tessellation and the corresponding Delaunay Triangulation defines the P2P overlay. A hierarchy of Voronoi diagrams is defined by exploiting clusters of objects paired with the same site of the Voronoi diagram. A new Voronoi diagram including the peers of the cluster is created so that the query resolution may be refined by a top down visit of the Voronoi hierarchy. The paper presents the proposed solution, analysis its complexity, and provides a set of experimental results.