k3_g6 := List([1..28], i -> []);

k3_g6[16, 1] := [ [ 9, 10, 15 ], [ 8, 12, 15 ], [ 8, 13, 14 ], [ 11, 13, 15 ], [ 9, 12, 14 ], [ 10, 11, 14 ], [ 10, 12, 13 ], [ 2, 3, 16 ], 
  [ 1, 5, 16 ], [ 1, 6, 7 ], [ 4, 6, 16 ], [ 2, 5, 7 ], [ 3, 4, 7 ], [ 3, 5, 6 ], [ 1, 2, 4 ], [ 8, 9, 11 ] ];

k3_g6[18, 1] := [ [ 10, 17, 18 ], [ 8, 12, 15 ], [ 13, 14, 17 ], [ 11, 13, 15 ], [ 9, 12, 14 ], [ 10, 11, 14 ], [ 10, 12, 13 ], [ 2, 16, 17 ], 
  [ 5, 16, 18 ], [ 1, 6, 7 ], [ 4, 6, 16 ], [ 2, 5, 7 ], [ 3, 4, 7 ], [ 3, 5, 6 ], [ 2, 4, 18 ], [ 8, 9, 11 ], [ 1, 3, 8 ], [ 1, 9, 15 ] ];

k3_g6[20, 1] := [ [ 10, 17, 18 ], [ 15, 19, 20 ], [ 13, 17, 19 ], [ 11, 13, 15 ], [ 9, 12, 14 ], [ 10, 11, 14 ], [ 10, 12, 13 ], [ 16, 17, 20 ], 
  [ 5, 16, 18 ], [ 1, 6, 7 ], [ 4, 6, 16 ], [ 5, 7, 20 ], [ 3, 4, 7 ], [ 5, 6, 19 ], [ 2, 4, 18 ], [ 8, 9, 11 ], [ 1, 3, 8 ], [ 1, 9, 15 ], [ 2, 3, 14 ], [ 2, 8, 12 ] ];

k3_g6[22, 1] := [ [ 10, 21, 22 ], [ 15, 20, 21 ], [ 13, 17, 19 ], [ 11, 13, 15 ], [ 9, 12, 14 ], [ 10, 11, 14 ], [ 10, 12, 13 ], [ 16, 17, 20 ], 
  [ 5, 16, 18 ], [ 1, 6, 7 ], [ 4, 6, 16 ], [ 5, 7, 20 ], [ 3, 4, 7 ], [ 5, 6, 19 ], [ 2, 4, 18 ], [ 8, 9, 11 ], [ 3, 8, 22 ], [ 9, 15, 22 ], [ 3, 14, 21 ], [ 2, 8, 12 ], [ 1, 2, 19 ], [ 1, 17, 18 ] ];

k3_g6[24, 1] := [ [ 10, 21, 22 ], [ 20, 23, 24 ], [ 17, 19, 23 ], [ 11, 13, 15 ], [ 9, 12, 14 ], [ 10, 11, 14 ], [ 10, 12, 13 ], [ 16, 17, 20 ], 
  [ 5, 16, 18 ], [ 1, 6, 7 ], [ 4, 6, 16 ], [ 5, 7, 20 ], [ 4, 7, 23 ], [ 5, 6, 19 ], [ 4, 18, 24 ], [ 8, 9, 11 ], [ 3, 8, 22 ], [ 9, 15, 22 ], [ 3, 14, 21 ], [ 2, 8, 12 ], [ 1, 19, 24 ], [ 1, 17, 18 ], [ 2, 3, 13 ], [ 2, 15, 21 ] ];

k3_g6[26, 1] := [ [ 22, 25, 26 ], [ 23, 24, 25 ], [ 17, 19, 23 ], [ 11, 13, 15 ], [ 9, 12, 14 ], [ 10, 11, 14 ], [ 10, 12, 13 ], [ 16, 17, 20 ], 
  [ 5, 16, 18 ], [ 6, 7, 25 ], [ 4, 6, 16 ], [ 5, 7, 20 ], [ 4, 7, 23 ], [ 5, 6, 19 ], [ 4, 18, 24 ], [ 8, 9, 11 ], [ 3, 8, 22 ], [ 9, 15, 22 ], [ 3, 14, 21 ], [ 8, 12, 26 ], [ 19, 24, 26 ], [ 1, 17, 18 ], [ 2, 3, 13 ], 
  [ 2, 15, 21 ], [ 1, 2, 10 ], [ 1, 20, 21 ] ];

k3_g6[28, 1] := [ [ 25, 26, 27 ], [ 24, 25, 28 ], [ 19, 23, 27 ], [ 11, 13, 15 ], [ 9, 12, 14 ], [ 10, 11, 14 ], [ 10, 12, 13 ], [ 16, 17, 20 ], 
  [ 5, 16, 18 ], [ 6, 7, 25 ], [ 4, 6, 16 ], [ 5, 7, 20 ], [ 4, 7, 23 ], [ 5, 6, 19 ], [ 4, 18, 24 ], [ 8, 9, 11 ], [ 8, 22, 27 ], [ 9, 15, 22 ], [ 3, 14, 21 ], [ 8, 12, 26 ], [ 19, 24, 26 ], [ 17, 18, 28 ], [ 3, 13, 28 ], 
  [ 2, 15, 21 ], [ 1, 2, 10 ], [ 1, 20, 21 ], [ 1, 3, 17 ], [ 2, 22, 23 ] ];