Before revision: We analyze the problem of quadtragulating a n-sided patch, with prescribed numbers of edge-subdivisions at its boundary , with a single internal irregular vertex (  none, when n = 4) breaking the otherwise fully regular lattice.
After revision: We analyze the problem of quadtragulating a n-sided patch, with prescribed numbers of edge-subdivisions at its boundary subdivided into a given number of edges, using a single irregular vertex ( none, when n = 4) breaking the otherwise fully regular lattice.