 For a given symmetry simplex, a generating point may be placed on any of the four vertices, 6 edges, 4 faces, or the interior volume.On each of these 15 elements there is a point whose images, reflected in the four mirrors, are the vertices of a uniform 4-polytope.The extended Schläfli symbols are made by a t followed by inclusion of one to four subscripts 0,1,2,3.