... pure two-dimensional and has onlyeight maximal faces. The case k = 3 is handled at the end of this section. Let k ≥ 4 and let Qkdenote the face poset of Ind(SG2,k) and let Ik+2be a (k ... even numbersor the odd numbers; and M: We say X is a middle vertex for all other cases.{3,5,7,9}{1,3,5,7}{2,4,6,8}{4,6,8,10}{2,4,6,9}{1,4,6,9}{3,5,7,10}Figure 1: SG4,2Figures 1 and ... copy ofKn+1,n+1 and a copy of DC2n+2 and add an edge connecting each v ertex i of Kn+1,n+1tothe vertex ciof DC2n+2. If 2 | n, take a copy of Kn+1,n+1 and a copy of Cn+1 and addedges...