The problem of parallel thread mapping is studied for the case of discrete orthogonal m-simplices. The possibility of a O(1) time recursive block-space map is analyzed from the point of view of parallel space efficiency and potential performance improvement. The 2-simplex and 3-simplex are analyzed as special cases where constant time maps are found, providing a potential improvement of up to 2x and 6x more efficient than a bounding-box approach, respectively.