enumerateVerticesDeltakDeltal :=
(

(*
vertexmatrix is
the matrix of the full dimensional point arrangement
*)
ClearAll[vertexmatrix];
vertexmatrix=
Transpose[
	Drop[
		Drop[
			Transpose[
				Flatten[
					Outer[
						Join,
						IdentityMatrix[k+1],
						IdentityMatrix[l+1],
						1],
					1]],
			{k+1}],
		{k+l+1}]];

(*
vertex[i] = USED vertices of simplex i 
the full dimensional point arrangement of (k+1)(l+1)
vertices
*)
ClearAll[vertex];
Do[
	vertex[i] = vertexmatrix[[i]],
	{i,(k+1)(l+1)}];

ClearAll[vertexmatrix]

)