The independent spanning trees (ISTs) problem is asked to find k spanning trees rooted at a designated vertex r such that, for any vertex v, all paths connecting r and v in k spanning trees are pairwise internally disjoint in the given graph. ISTs have numerous applications in networks such as reliable communication protocols, data broadcasting and secure message distribution. In the past, most of the results focused on constructing k-ISTs on symmetric networks. While the existence of asymmetry makes the k-ISTs problem even harder than its symmetric counterpart, we have derived linear time algorithms for solving 3-ISTs rooted at an arbitrary vertex of recursive transpose-connected 4-cycle-pyramids.