More on Decomposable \(3-(12, 6, 4)\) Designs

In a previous paper, all non-isomorphic decomposable \(3-(12,6,4)\) designs without repeated blocks were determined. These results are extended here by allowing repeated blocks. Under this condition, there are \(26\) non-isomorphic decomposable \(3-(12,6,4)\) designs, of which \(14\) have repeated blocks. Key blocks and point permutations for models of these designs are given, along with descriptions of their automorphism groups.