Virtual network embedding (VNE) can effectively deploy virtual networks (VNs) onto shared substrate network (SN) resources. However, with the consistent changing scalability and diversity demands of VNs, traditional VNE methods prove to be a challenging task for current cloud service platforms. Thus, we model a repeatable multi-dimensional virtual network embedding (RMD-VNE) problem for implementing multi-dimensional virtual networks (MD-VNs) that involves real servers, virtual machines, containers, and network simulators. The MD-VN is preprocessed and embedded via a heuristic method denoted as ReMiDvne. Following its transformation for the containers and simulation networks, the MD-VN topology undergoes a process of coarsening, partitioning, and uncoarsening. ReMiDvne then applies a topology-aware repeatable embedding solution to complete the embedding stage. Experimental results demonstrate that ReMiDvne outperforms seven baseline approaches through small-, 1,000- and 10,000-scale VNE simulation experiments. Remarkably, ReMiDvne improves the average rates of acceptance ratio, revenue, and revenue-cost ratio by up to 40.45, 40.45, and 299.03 percent, respectively, and reduces the average rate of cost by up to 64.16 percent. Furthermore, real-world VNE experiments are conducted based on the OpenStack platform. The results reveal the ability of ReMiDvne to efficiently reduce communication costs by up to 45.93 and 63.43 percent for download and upload, respectively.