M4 for hard hexagon without Effect of Orders:
Type 1 has 6 children: 2 3 4 5 6 7 
Type 2 has 5 children: 2 8 9 10 11 
Type 3 has 5 children: 12 3 13 14 15 
Type 4 has 5 children: 16 17 4 18 19 
Type 5 has 5 children: 20 21 5 22 23 
Type 6 has 5 children: 24 25 26 6 27 
Type 7 has 5 children: 28 29 30 31 7 
Type 8 has 5 children: 12 3 13 32 15 
Type 9 has 4 children: 16 17 4 33 
Type 10 has 4 children: 24 34 6 27 
Type 11 has 5 children: 28 29 35 31 7 
Type 12 has 5 children: 2 8 9 36 11 
Type 13 has 5 children: 16 17 4 18 37 
Type 14 has 4 children: 20 21 5 38 
Type 15 has 4 children: 28 29 39 7 
Type 16 has 4 children: 2 8 9 40 
Type 17 has 5 children: 12 3 13 14 41 
Type 18 has 5 children: 20 21 5 22 42 
Type 19 has 4 children: 25 26 6 43 
Type 20 has 4 children: 44 3 13 14 
Type 21 has 5 children: 45 17 4 18 19 
Type 22 has 5 children: 46 25 26 6 27 
Type 23 has 4 children: 47 30 31 7 
Type 24 has 4 children: 2 48 10 11 
Type 25 has 4 children: 49 4 18 19 
Type 26 has 5 children: 50 21 5 22 23 
Type 27 has 5 children: 28 51 30 31 7 
Type 28 has 5 children: 2 8 52 10 11 
Type 29 has 4 children: 12 3 53 15 
Type 30 has 4 children: 54 5 22 23 
Type 31 has 5 children: 24 55 26 6 27 
Type 32 has 3 children: 20 21 5 
Type 33 has 4 children: 20 21 5 22 
Type 34 has 4 children: 21 5 22 23 
Type 35 has 3 children: 5 22 23 
Type 36 has 3 children: 24 6 27 
Type 37 has 3 children: 25 26 6 
Type 38 has 4 children: 25 26 6 27 
Type 39 has 4 children: 24 26 6 27 
Type 40 has 4 children: 28 29 31 7 
Type 41 has 3 children: 28 29 7 
Type 42 has 3 children: 30 31 7 
Type 43 has 4 children: 28 30 31 7 
Type 44 has 4 children: 2 8 9 11 
Type 45 has 3 children: 2 8 9 
Type 46 has 3 children: 2 10 11 
Type 47 has 4 children: 2 8 10 11 
Type 48 has 4 children: 12 3 13 15 
Type 49 has 4 children: 12 3 13 14 
Type 50 has 3 children: 3 13 14 
Type 51 has 3 children: 12 3 15 
Type 52 has 3 children: 16 17 4 
Type 53 has 4 children: 16 17 4 18 
Type 54 has 4 children: 17 4 18 19 
Type 55 has 3 children: 4 18 19