1. A volumetric vector addressing system comprising: a database for storing a set of multi-dimensional vector addresses and metadata describing the multi-dimensional vector addresses as defined from an origin of a multidimensional shared virtual environment, the metadata including: a set of multi-dimensional volume definitions associated with a subset of multidimensional vector addresses in the set of multi-dimensional vector addresses, wherein a multi-dimensional volume definition associated with a multidimensional vector address defines a container; and a set of computing resource addresses associated with a set of containers formed from a subset of multi-dimensional volume definitions in the set of multidimensional volume definitions; a network interface configured to receive a computing resource request from a computing device operating within the a multi-dimensional shared virtual environment, the request including a multi-dimensional vector address and provide a translation from the multidimensional vector address to an associated set of computing resource addresses; a processor managing the multi-dimensional shared virtual environment and configured to: receive the request from the network interface for computing resources including a multi-dimensional vector address; determine a container that contains the multi-dimensional vector address based at least in part on the metadata; determine the associated set of computing resource addresses associated with the container; generate a message including the translation from the multidimensional vector address to the associated set of computing resource addresses; receive a request to associate a new container with a requested set of computing resources, the container defining a requested multi-dimensional vector address and a requested volume definition; determine a lack of overlap of the new container with the set of containers; add the requested multi-dimensional vector address to the set of multidimensional vector addresses; and create additional metadata describing the requested multi-dimensional vector address including the requested volume definition and the requested set of computing resources.