An elementary proof of the unicity of the 4-(11, 6, 3) design

In the unique Steiner system S(5,6, 12) the blocks, which do not contain a fixed point x, give us the blocks of a 4-(11,6,3) design, called the external contraction of S(5,6,12) at x . We prove that two distinct contractions are isomorphic and that each 4-(11, 6, 3) d: sign can be embedded in S(5,6,12) . Moreover, the blocking sets of the 4-(11,6, 3) design are completely characterized.