Another complete invariant for Steiner triple systems of order 15

Abstract

In this note, the 80 non-isomorphic triple systems on 15 points are revisited from the viewpoint of the convex hull of the characteristic vectors of their blocks. The main observation is that the numbers, of facets of these 80 polyhedra are all different, thus producing a new proof of the non-isomorphism of these triple systems. The space dimension of these polyhedra is also discussed. Finally, we observe the large number of facets of some of these polyhedra with few vertices, in relation with the upper bound problem for combinatorial polyhedra. # 2005 Wiley Periodicals, Inc. J Combin Designs 13: [388][389][390][391] 2005