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Let \(G = (V, E)\) be a graph with \(n\) vertices. A bijection \(f : V \to \{1, 2, \dots, n\}\) is called a distance magic labeling of \(G\) if there exists an integer \(k\) such that \(\sum_{u \in N(v)}f (u) = k\) for all \(v \in V\), where \(N(v)\) is the set of all vertices adjacent to \(v\). Any graph which admits a distance magic labeling is a distance magic graph. The existence of regular distance magic graphs of even order was solved completely in a paper by Fronček, Kovář, and Kovářová. In two recent papers, the existence of \(4\)-regular and of \((n-3)\)-regular distance magic graphs of odd order was also settled completely. In this paper, we provide a similar classification of all feasible odd orders of \(r\)-regular distance magic graphs when \(r=6,8,10,12\). Even though some nonexistence proofs for small orders are done by brute force enumeration, all the existence proofs are constructive.