Distributed Hash Tables (DHT) proved to be scalable decentralized systems providing efficient resource location. This paper concentrates on efficiency and resilience to node failures of DHT systems and presents a novel model of a distributed hash table based on a hierarchical hypercube geometry, called HyCube. The DHT geometry, the choice of the metric defining logical distances between nodes, and the routing algorithm have fundamental influence on routing efficiency and resilience. The use of the one-dimensional model (placing the nodes logically on a ring) allows the nodes to maintain sets of references called sequential neighbors - certain numbers of neighbors that are the closest existing nodes in both directions on the ring. Such a model yields a very high level of resilience to node failures. The new approach, presented in the paper, employs a variable multi-dimensional metric adopting the Steinhaus transform. Routing, lookup and search algorithms are discussed, as well as routing table nodes selection and self-organization techniques. It is shown that the new approach allows reaching a higher level of resilience to node failures, as well as a shorter average routing path length than with the use of the sequential neighbors sets.