M6 for hard hexagon with Effect of Orders: Type 1 has 6 children: 2 3 4 5 6 7 Type 2 has 3 children: 8 9 10 Type 3 has 4 children: 11 12 13 14 Type 4 has 4 children: 15 16 17 18 Type 5 has 4 children: 19 20 21 22 Type 6 has 4 children: 23 24 25 26 Type 7 has 5 children: 27 28 29 30 31 Type 8 has 3 children: 8 32 33 Type 9 has 4 children: 11 34 35 36 Type 10 has 4 children: 27 41 42 43 Type 11 has 3 children: 44 9 45 Type 12 has 4 children: 46 12 47 48 Type 13 has 4 children: 49 16 50 51 Type 14 has 3 children: 54 28 55 Type 15 has 3 children: 56 57 58 Type 16 has 4 children: 59 60 13 61 Type 17 has 4 children: 62 63 17 64 Type 18 has 4 children: 65 20 66 67 Type 19 has 3 children: 70 71 72 Type 20 has 4 children: 73 74 75 18 Type 21 has 4 children: 76 77 21 78 Type 22 has 4 children: 79 24 80 81 Type 23 has 3 children: 87 88 89 Type 24 has 4 children: 90 91 92 22 Type 25 has 4 children: 93 94 25 95 Type 26 has 4 children: 96 97 30 98 Type 27 has 3 children: 99 100 10 Type 28 has 4 children: 101 102 103 14 Type 29 has 3 children: 104 105 106 Type 30 has 4 children: 107 108 109 26 Type 31 has 5 children: 110 111 112 113 31 Type 32 has 4 children: 11 34 35 36 Type 33 has 4 children: 27 41 42 43 Type 34 has 4 children: 46 12 47 48 Type 35 has 4 children: 49 16 50 116 Type 36 has 3 children: 54 28 55 Type 37 has 4 children: 59 60 13 61 Type 38 has 4 children: 62 63 17 118 Type 39 has 3 children: 121 25 95 Type 40 has 4 children: 96 122 30 98 Type 41 has 4 children: 101 102 123 14 Type 42 has 3 children: 125 109 26 Type 43 has 5 children: 110 111 126 113 31 Type 44 has 3 children: 8 32 33 Type 45 has 4 children: 27 41 128 43 Type 46 has 3 children: 44 9 45 Type 47 has 4 children: 49 16 50 51 Type 48 has 3 children: 54 28 130 Type 49 has 3 children: 56 57 131 Type 50 has 4 children: 62 63 17 64 Type 51 has 4 children: 65 20 66 132 Type 52 has 4 children: 73 74 75 18 Type 53 has 4 children: 76 77 21 134 Type 54 has 3 children: 99 100 10 Type 55 has 4 children: 110 111 137 31 Type 56 has 3 children: 8 32 138 Type 57 has 4 children: 11 34 35 139 Type 58 has 3 children: 27 41 140 Type 59 has 3 children: 44 9 141 Type 60 has 4 children: 46 12 47 142 Type 61 has 3 children: 143 28 144 Type 62 has 3 children: 145 57 146 Type 63 has 4 children: 59 60 13 147 Type 64 has 4 children: 65 20 66 67 Type 65 has 3 children: 149 71 72 Type 66 has 4 children: 76 77 21 78 Type 67 has 4 children: 79 24 80 150 Type 68 has 4 children: 90 91 92 22 Type 69 has 4 children: 93 94 25 152 Type 70 has 3 children: 154 9 155 Type 71 has 4 children: 156 12 47 157 Type 72 has 4 children: 158 16 50 51 Type 73 has 2 children: 159 160 Type 74 has 4 children: 161 60 13 162 Type 75 has 4 children: 163 63 17 64 Type 76 has 3 children: 164 165 72 Type 77 has 4 children: 166 74 75 18 Type 78 has 4 children: 79 24 80 81 Type 79 has 3 children: 169 88 89 Type 80 has 4 children: 93 94 25 95 Type 81 has 4 children: 170 97 30 98 Type 82 has 4 children: 107 108 109 26 Type 83 has 4 children: 173 112 113 31 Type 84 has 3 children: 8 174 33 Type 85 has 4 children: 11 175 176 36 Type 86 has 4 children: 27 177 42 43 Type 87 has 3 children: 178 179 13 Type 88 has 4 children: 180 181 17 64 Type 89 has 4 children: 182 20 66 67 Type 90 has 2 children: 183 184 Type 91 has 4 children: 185 186 75 18 Type 92 has 4 children: 187 77 21 78 Type 93 has 3 children: 189 190 89 Type 94 has 4 children: 191 91 92 22 Type 95 has 4 children: 96 97 30 98 Type 96 has 3 children: 99 192 10 Type 97 has 3 children: 195 105 106 Type 98 has 5 children: 110 196 112 113 31 Type 99 has 3 children: 8 32 33 Type 100 has 4 children: 11 34 197 36 Type 101 has 3 children: 44 9 45 Type 102 has 4 children: 46 12 200 48 Type 103 has 4 children: 49 16 201 202 Type 104 has 3 children: 203 204 18 Type 105 has 4 children: 205 206 21 78 Type 106 has 4 children: 207 24 80 81 Type 107 has 2 children: 209 210 Type 108 has 4 children: 211 212 92 22 Type 109 has 4 children: 213 94 25 95 Type 110 has 3 children: 99 100 10 Type 111 has 4 children: 101 214 215 14 Type 112 has 3 children: 216 217 106 Type 113 has 4 children: 218 108 109 26 Type 114 has 4 children: 62 63 17 118 Type 115 has 3 children: 121 25 95 Type 116 has 3 children: 65 20 66 Type 117 has 4 children: 73 74 75 18 Type 118 has 4 children: 65 20 66 67 Type 119 has 4 children: 76 77 21 78 Type 120 has 3 children: 77 21 78 Type 121 has 3 children: 91 92 22 Type 122 has 2 children: 105 106 Type 123 has 3 children: 49 16 201 Type 124 has 3 children: 24 80 81 Type 125 has 2 children: 92 22 Type 126 has 2 children: 217 106 Type 127 has 3 children: 96 30 98 Type 128 has 2 children: 109 26 Type 129 has 4 children: 76 77 21 134 Type 130 has 4 children: 110 111 137 31 Type 131 has 3 children: 27 41 140 Type 132 has 3 children: 79 24 80 Type 133 has 4 children: 90 91 92 22 Type 134 has 4 children: 79 24 80 81 Type 135 has 4 children: 93 94 25 95 Type 136 has 3 children: 94 25 95 Type 137 has 3 children: 108 109 26 Type 138 has 4 children: 27 41 42 43 Type 139 has 3 children: 54 28 55 Type 140 has 4 children: 110 111 113 31 Type 141 has 4 children: 27 41 220 43 Type 142 has 3 children: 54 28 130 Type 143 has 3 children: 99 100 10 Type 144 has 3 children: 110 111 31 Type 145 has 3 children: 8 32 138 Type 146 has 3 children: 27 41 221 Type 147 has 3 children: 143 28 222 Type 148 has 4 children: 93 94 25 152 Type 149 has 3 children: 154 9 223 Type 150 has 3 children: 97 30 98 Type 151 has 4 children: 107 108 109 26 Type 152 has 4 children: 96 97 30 98 Type 153 has 4 children: 110 112 113 31 Type 154 has 3 children: 8 32 33 Type 155 has 3 children: 27 41 43 Type 156 has 3 children: 44 9 45 Type 157 has 3 children: 54 28 225 Type 158 has 3 children: 56 57 226 Type 159 has 3 children: 8 32 227 Type 160 has 4 children: 11 34 35 228 Type 161 has 3 children: 44 9 229 Type 162 has 2 children: 230 28 Type 163 has 3 children: 145 57 231 Type 164 has 2 children: 232 9 Type 165 has 4 children: 156 12 47 233 Type 166 has 2 children: 234 160 Type 167 has 4 children: 173 112 113 31 Type 168 has 3 children: 27 42 43 Type 169 has 3 children: 236 179 13 Type 170 has 2 children: 99 10 Type 171 has 3 children: 8 32 33 Type 172 has 4 children: 11 34 237 36 Type 173 has 3 children: 99 100 10 Type 174 has 4 children: 11 34 35 36 Type 175 has 4 children: 46 12 47 48 Type 176 has 4 children: 49 16 50 240 Type 177 has 4 children: 101 102 241 14 Type 178 has 3 children: 44 9 242 Type 179 has 4 children: 46 12 47 243 Type 180 has 2 children: 244 57 Type 181 has 4 children: 59 60 13 245 Type 182 has 3 children: 246 71 72 Type 183 has 3 children: 247 12 47 Type 184 has 4 children: 248 16 50 51 Type 185 has 1 children: 249 Type 186 has 4 children: 250 60 13 251 Type 187 has 3 children: 252 165 72 Type 188 has 3 children: 8 174 33 Type 189 has 2 children: 254 13 Type 190 has 4 children: 255 181 17 64 Type 191 has 2 children: 256 184 Type 192 has 4 children: 11 34 257 36 Type 193 has 3 children: 44 9 45 Type 194 has 4 children: 46 12 259 48 Type 195 has 3 children: 260 204 18 Type 196 has 3 children: 101 214 14 Type 197 has 4 children: 49 16 50 261 Type 198 has 4 children: 59 60 13 61 Type 199 has 4 children: 62 63 17 263 Type 200 has 4 children: 49 16 50 51 Type 201 has 4 children: 62 63 17 64 Type 202 has 4 children: 65 20 66 265 Type 203 has 3 children: 266 60 13 Type 204 has 4 children: 267 63 17 64 Type 205 has 2 children: 268 72 Type 206 has 4 children: 269 74 75 18 Type 207 has 3 children: 270 88 89 Type 208 has 4 children: 11 175 271 36 Type 209 has 3 children: 272 17 64 Type 210 has 4 children: 273 20 66 67 Type 211 has 1 children: 274 Type 212 has 4 children: 275 276 75 18 Type 213 has 3 children: 277 190 89 Type 214 has 4 children: 46 12 200 48 Type 215 has 3 children: 49 16 279 Type 216 has 2 children: 280 18 Type 217 has 4 children: 281 206 21 78 Type 218 has 2 children: 282 210 Type 219 has 3 children: 96 30 98 Type 220 has 2 children: 109 26 Type 221 has 4 children: 110 111 113 31 Type 222 has 3 children: 110 111 31 Type 223 has 3 children: 27 41 43 Type 224 has 4 children: 11 34 257 36 Type 225 has 4 children: 110 111 137 31 Type 226 has 3 children: 27 41 140 Type 227 has 4 children: 27 41 42 43 Type 228 has 3 children: 54 28 55 Type 229 has 3 children: 27 41 43 Type 230 has 3 children: 99 100 10 Type 231 has 2 children: 27 41 Type 232 has 3 children: 8 32 33 Type 233 has 2 children: 54 28 Type 234 has 2 children: 8 32 Type 235 has 4 children: 11 34 35 36 Type 236 has 2 children: 44 9 Type 237 has 4 children: 49 16 50 261 Type 238 has 4 children: 46 12 200 48 Type 239 has 4 children: 62 63 17 118 Type 240 has 3 children: 65 20 66 Type 241 has 3 children: 49 16 201 Type 242 has 4 children: 27 41 220 43 Type 243 has 3 children: 54 28 130 Type 244 has 3 children: 8 32 138 Type 245 has 2 children: 143 28 Type 246 has 2 children: 154 9 Type 247 has 3 children: 44 9 45 Type 248 has 2 children: 56 57 Type 249 has 3 children: 11 34 35 Type 250 has 2 children: 44 9 Type 251 has 1 children: 28 Type 252 has 1 children: 9 Type 253 has 4 children: 46 12 47 48 Type 254 has 3 children: 46 12 47 Type 255 has 1 children: 57 Type 256 has 2 children: 12 47 Type 257 has 3 children: 49 16 50 Type 258 has 4 children: 59 60 13 61 Type 259 has 4 children: 49 16 50 51 Type 260 has 2 children: 60 13 Type 261 has 3 children: 65 20 66 Type 262 has 4 children: 73 74 75 18 Type 263 has 4 children: 65 20 66 67 Type 264 has 4 children: 76 77 21 134 Type 265 has 3 children: 79 24 80 Type 266 has 3 children: 44 9 229 Type 267 has 2 children: 145 57 Type 268 has 3 children: 156 12 47 Type 269 has 1 children: 160 Type 270 has 2 children: 179 13 Type 271 has 3 children: 49 16 50 Type 272 has 3 children: 59 60 13 Type 273 has 2 children: 71 72 Type 274 has 3 children: 16 50 51 Type 275 has 0 children: Type 276 has 3 children: 60 13 251 Type 277 has 1 children: 13 Type 278 has 3 children: 62 63 17 Type 279 has 4 children: 62 63 17 64 Type 280 has 3 children: 63 17 64 Type 281 has 1 children: 72 Type 282 has 2 children: 17 64