k3_g4 := List([1..12], i -> []);

k3_g4[8, 1] := [ [ 6, 7, 8 ], [ 5, 6, 7 ], [ 4, 5, 6 ], [ 3, 7, 8 ], [ 2, 3, 8 ], [ 1, 2, 3 ], [ 1, 2, 4 ], [ 1, 4, 5 ] ];

k3_g4[10, 1] := [ [ 8, 9, 10 ], [ 6, 7, 9 ], [ 4, 5, 6 ], [ 3, 7, 8 ], [ 3, 8, 9 ], [ 2, 3, 10 ], [ 2, 4, 10 ], [ 1, 4, 5 ], [ 1, 2, 5 ], [ 1, 6, 7 ] ];

k3_g4[12, 1] := [ [ 10, 11, 12 ], [ 7, 9, 11 ], [ 4, 5, 6 ], [ 3, 7, 8 ], [ 3, 8, 9 ], [ 3, 10, 11 ], [ 2, 4, 10 ], [ 4, 5, 12 ], [ 2, 5, 12 ], [ 1, 6, 7 ], [ 1, 2, 6 ], [ 1, 8, 9 ] ];