In order to deliver the computational power required by real-time manipulation and display of multidimensional objects, we present a massively parallel octree architecture, based on a new Interconnection Network, the Partitionable Spanning Multibus Hypercube (PSMH). Its goal is, to use one Processing Element per obel (object element), as opposed to one Processing Element per voxel (volume element). The underlying idea of the PSMH, is to take advantage of the data hierarchical ordering to reduce the computational cost. As a basic tool, we first derive a routing algorithm for the case of an object shift. Its running time is of order O(max(n3, m)), for an 8n PSMH, where m is the message length in bits. As we do not consider voxels but obels, we design a compaction algorithm, which meets the routing requirements. We get a compression ratio of O(2n). This is followed by a parallel neighbor finding technique, to account for the compaction in the routing operations.