Abstract—The generalized Fibonacci cubes (abbreviated to GFCs) [4] were recently proposed as a class of interconnection topologies, which cover a spectrum ranging from regular graphs such as the hypercube to semiregular graphs such as the second-order Fibonacci cube in [1]. It has been shown that the kth order GFC of dimension n + k is equivalent to an n-cube for 0 ≤n < k; and it is a proper subgraph of an n-cube for n≥k [4]. Thus, a kth order GFC of dimension n + k can be obtained from the n-cube for all n≥k by removing certain nodes from an n-cube. This problem is very simple when no faulty node exists in an n-cube; but it becomes very complex if some faulty nodes appear in an n-cube. In this paper, we first consider the following open problem: How can a maximal (in terms of the number of nodes) generalized Fibonacci cube be distinguished from a faulty hypercube [3] which can also be considered as a Fault-tolerant embedding in hypercubes. Then, we shall show how to directly embed a GFC into a faulty hypercube and prove that if no more than three faulty nodes exist, then an $\left\lfloor {{\textstyle{n \over 2}}} \right\rfloor {\rm th}$ order GFC of dimension $n+\left\lfloor {{\textstyle{n \over 2}}} \right\rfloor $ can be directly embedded into an n-cube in the worst case, for n = 4 or n≥ 6.