M4 for hard hexagon with Effect of Orders:
Type 1 has 6 children: 2 3 4 5 6 7 
Type 2 has 3 children: 2 8 9 
Type 3 has 4 children: 10 3 11 12 
Type 4 has 4 children: 13 14 4 15 
Type 5 has 4 children: 16 17 5 18 
Type 6 has 4 children: 19 20 6 21 
Type 7 has 5 children: 22 23 24 25 7 
Type 8 has 4 children: 10 3 11 12 
Type 9 has 4 children: 22 23 25 7 
Type 10 has 3 children: 2 8 9 
Type 11 has 4 children: 13 14 4 15 
Type 12 has 3 children: 22 23 7 
Type 13 has 3 children: 2 8 26 
Type 14 has 4 children: 10 3 11 27 
Type 15 has 4 children: 16 17 5 18 
Type 16 has 3 children: 28 3 11 
Type 17 has 4 children: 29 14 4 15 
Type 18 has 4 children: 19 20 6 21 
Type 19 has 3 children: 31 4 15 
Type 20 has 4 children: 32 17 5 18 
Type 21 has 4 children: 22 24 25 7 
Type 22 has 3 children: 2 8 9 
Type 23 has 4 children: 10 3 33 12 
Type 24 has 3 children: 34 5 18 
Type 25 has 4 children: 35 20 6 21 
Type 26 has 4 children: 22 23 25 7 
Type 27 has 3 children: 22 23 7 
Type 28 has 3 children: 2 8 9 
Type 29 has 2 children: 2 8 
Type 30 has 4 children: 10 3 11 12 
Type 31 has 3 children: 10 3 11 
Type 32 has 2 children: 3 11 
Type 33 has 4 children: 13 14 4 15 
Type 34 has 3 children: 14 4 15 
Type 35 has 2 children: 4 15