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Gaussian cubes (GC) are a family of interconnection topologies in which the interconnection density and algorithmic efficiency are linked by a common parameter, the variation of which can scale routing performance according to traffic loads without changing the routing algorithm. However, there is no existing fault-tolerant routing strategy for GC as well as node/link diluted cubes. In this paper, the void is filled for GC with an algorithm based on a new topology: Gaussian tree (GT). With a many-to-one mapping, the original problem is converted into routing in GT, which is found to be more definite and predictable. A new approach to categorizing faulty components is presented to overcome the problem of low node availability and the maximum number of faults tolerable is given. The algorithm is livelock free and generates deadlock-free routes, which are at most 2F hops longer than the optimal route in a fault-free setting, if F faults are encountered. Finally, simulation is done to show the algorithm's performance, demonstrating its contribution to making GC a more fault-tolerant topology.