it is known that a pg("n",2) can be coordinatized with (gf(2)), i.e. a bit string of length "n" + 1. pg(3,2) can therefore be coordinatized with 4-bit strings. a common mapping between these coordinates and the tetrahedral representation above is for tetrehedron vertices to have hamming weight 1, such as 0001, 0010, etc., and for other points to be the xor thereof. thus edge midpoints get hamming weight 2, face centers get hamming weight 3, and the body center gets hamming weight 4.