k3_g5 := List([1..20], i -> []);

k3_g5[12, 1] := [ [ 8, 11, 12 ], [ 5, 9, 11 ], [ 7, 10, 11 ], [ 5, 6, 10 ], [ 2, 4, 12 ], [ 4, 7, 8 ], [ 3, 6, 12 ], [ 1, 6, 9 ], [ 2, 8, 10 ], [ 3, 4, 9 ], [ 1, 2, 3 ], [ 1, 5, 7 ] ];

k3_g5[14, 1] := [ [ 8, 13, 14 ], [ 9, 11, 13 ], [ 7, 10, 11 ], [ 5, 6, 10 ], [ 4, 12, 13 ], [ 4, 7, 8 ], [ 3, 6, 12 ], [ 1, 6, 9 ], [ 2, 8, 10 ], [ 3, 4, 9 ], [ 2, 3, 14 ], [ 5, 7, 14 ], [ 1, 2, 5 ], [ 1, 11, 12 ] ];

k3_g5[16, 1] := [ [ 14, 15, 16 ], [ 11, 13, 15 ], [ 7, 10, 11 ], [ 5, 6, 10 ], [ 4, 12, 13 ], [ 4, 7, 8 ], [ 3, 6, 12 ], [ 6, 9, 15 ], 
  [ 8, 10, 16 ], [ 3, 4, 9 ], [ 2, 3, 14 ], [ 5, 7, 14 ], [ 2, 5, 16 ], [ 1, 11, 12 ], [ 1, 2, 8 ], [ 1, 9, 13 ] ];

k3_g5[18, 1] := [ [ 16, 17, 18 ], [ 13, 15, 17 ], [ 7, 10, 11 ], [ 5, 6, 10 ], [ 4, 12, 13 ], [ 4, 7, 8 ], [ 3, 6, 12 ], [ 6, 9, 15 ], 
  [ 8, 10, 16 ], [ 3, 4, 9 ], [ 3, 14, 17 ], [ 5, 7, 14 ], [ 2, 5, 16 ], [ 11, 12, 18 ], [ 2, 8, 18 ], [ 1, 9, 13 ], [ 1, 2, 11 ], [ 1, 14, 15 ] ];

k3_g5[20, 1] := [ [ 18, 19, 20 ], [ 15, 17, 19 ], [ 7, 10, 11 ], [ 5, 6, 10 ], [ 4, 12, 13 ], [ 4, 7, 8 ], [ 3, 6, 12 ], [ 6, 9, 15 ], 
  [ 8, 10, 16 ], [ 3, 4, 9 ], [ 3, 14, 17 ], [ 5, 7, 14 ], [ 5, 16, 19 ], [ 11, 12, 18 ], [ 2, 8, 18 ], [ 9, 13, 20 ], [ 2, 11, 20 ], [ 1, 14, 15 ], [ 1, 2, 13 ], [ 1, 16, 17 ] ];