133 Hilbert basis elements 219 lattice points in polytope (Hilbert basis elements of degree 1) 319 extreme rays 4134 support hyperplanes 5 6embedding dimension = 9 7rank = 9 (maximal) 8external index = 4 9internal index = 1 10original monoid is not integrally closed in chosen lattice 11 12size of triangulation = 281 13resulting sum of |det|s = 425 14 15grading: 161 1 1 1 1 1 1 1 1 17with denominator = 4 18 19degrees of extreme rays: 201:19 21 22Hilbert basis elements are not of degree 1 23 24multiplicity = 425 25 26Hilbert series: 271 10 49 137 161 63 4 28denominator with 9 factors: 291:9 30 31degree of Hilbert Series as rational function = -3 32 33Hilbert polynomial: 3440320 142512 216092 191156 112105 46088 14098 3284 425 35with common denominator = 40320 36 37*********************************************************************** 38 3919 lattice points in polytope (Hilbert basis elements of degree 1): 40 0 0 0 0 1 1 1 0 1 41 0 0 1 1 1 1 0 0 0 42 0 1 0 0 1 1 1 0 0 43 0 1 0 1 1 0 0 0 1 44 0 1 0 1 1 1 0 0 0 45 0 1 1 0 1 0 1 0 0 46 0 1 1 0 1 1 0 0 0 47 0 1 1 1 0 0 1 0 0 48 0 1 1 1 1 0 0 0 0 49 1 0 0 1 0 1 1 0 0 50 1 0 0 1 1 1 0 0 0 51 1 0 1 0 0 0 0 1 1 52 1 0 1 0 0 1 0 1 0 53 1 0 1 1 1 0 0 0 0 54 1 1 0 0 0 1 0 0 1 55 1 1 0 0 1 0 1 0 0 56 1 1 0 1 0 0 0 1 0 57 1 1 1 0 1 0 0 0 0 58 1 1 1 1 0 0 0 0 0 59 6014 further Hilbert basis elements of higher degree: 61 1 1 0 1 1 2 1 0 1 62 1 1 0 1 2 1 1 0 1 63 2 1 1 1 1 1 0 1 0 64 1 3 1 1 2 1 2 0 1 65 2 2 0 2 2 2 1 0 1 66 2 2 1 1 1 1 1 1 2 67 2 2 1 1 1 2 1 1 1 68 2 2 2 2 1 0 1 1 1 69 2 2 2 2 2 0 0 1 1 70 3 1 1 1 1 2 1 1 1 71 3 2 1 1 1 1 1 1 1 72 3 2 2 1 1 1 0 1 1 73 2 3 1 2 2 1 2 1 2 74 3 3 2 3 2 0 1 1 1 75 7619 extreme rays: 77 0 0 0 0 1 1 1 0 1 78 0 0 1 1 1 1 0 0 0 79 0 1 0 0 1 1 1 0 0 80 0 1 0 1 1 0 0 0 1 81 0 1 0 1 1 1 0 0 0 82 0 1 1 0 1 0 1 0 0 83 0 1 1 0 1 1 0 0 0 84 0 1 1 1 0 0 1 0 0 85 0 1 1 1 1 0 0 0 0 86 1 0 0 1 0 1 1 0 0 87 1 0 0 1 1 1 0 0 0 88 1 0 1 0 0 0 0 1 1 89 1 0 1 0 0 1 0 1 0 90 1 0 1 1 1 0 0 0 0 91 1 1 0 0 0 1 0 0 1 92 1 1 0 0 1 0 1 0 0 93 1 1 0 1 0 0 0 1 0 94 1 1 1 0 1 0 0 0 0 95 1 1 1 1 0 0 0 0 0 96 97134 support hyperplanes: 98 -11 5 9 -3 5 13 1 9 -7 99 -7 -3 1 9 17 5 -7 1 5 100 -7 1 5 1 1 9 5 5 -3 101 -7 1 9 -3 13 17 -7 9 -11 102 -5 3 5 -1 1 5 1 3 -3 103 -3 1 -3 5 5 1 -3 5 1 104 -3 1 1 1 1 1 1 1 1 105 -3 1 3 -1 1 3 1 3 -1 106 -3 1 3 1 -1 3 3 1 -1 107 -3 3 -1 1 3 5 -3 -1 5 108 -3 5 -3 5 1 -3 1 9 1 109 -3 5 -3 5 1 1 -3 5 1 110 -1 -5 -1 7 7 3 -1 -1 3 111 -1 -3 1 3 5 -1 -1 1 5 112 -1 -1 -1 3 3 -1 -1 3 3 113 -1 -1 1 1 1 -1 1 1 3 114 -1 -1 2 0 0 1 2 2 1 115 -1 -1 3 -1 -1 3 3 3 3 116 -1 -1 3 -1 1 1 1 3 1 117 -1 0 1 0 0 1 1 1 0 118 -1 1 -1 1 1 -1 1 3 1 119 -1 1 -1 1 1 1 -1 1 1 120 -1 1 -1 1 1 1 -1 3 -1 121 -1 1 -1 1 1 3 -1 -1 3 122 -1 1 -1 1 1 3 -1 5 -3 123 -1 1 -1 2 1 0 -1 2 0 124 -1 1 -1 3 1 -1 -1 3 1 125 -1 1 0 0 1 2 -1 3 -2 126 -1 1 0 1 0 0 0 1 0 127 -1 1 0 2 0 -1 0 2 1 128 -1 1 1 -1 1 1 1 1 -1 129 -1 1 1 -1 1 3 -1 1 -1 130 -1 1 1 0 0 1 0 1 -1 131 -1 1 1 1 -1 1 1 1 -1 132 -1 1 2 0 0 1 0 0 -1 133 -1 1 2 1 0 0 0 -1 0 134 -1 1 4 2 0 -1 0 -2 1 135 -1 3 -5 3 3 -1 -1 7 -1 136 -1 3 -1 -1 3 -1 3 3 -1 137 -1 3 -1 1 1 -1 1 3 -1 138 -1 3 -1 3 -1 -1 -1 3 3 139 -1 3 -1 3 -1 -1 3 3 -1 140 -1 3 3 -1 -1 3 -1 -1 -1 141 0 -2 3 -1 2 1 0 3 1 142 0 -1 0 1 1 0 0 0 1 143 0 -1 1 0 1 0 0 1 1 144 0 0 0 0 0 0 0 0 1 145 0 0 0 0 0 0 0 1 0 146 0 0 0 0 0 0 1 0 0 147 0 0 0 0 0 1 0 0 0 148 0 0 0 0 1 -1 1 1 1 149 0 0 0 1 0 0 0 0 0 150 0 0 0 1 1 0 -1 0 0 151 0 0 1 -1 0 1 0 1 1 152 0 0 1 0 0 0 0 0 0 153 0 0 1 0 1 1 -1 0 -1 154 0 0 1 1 -1 0 1 -1 0 155 0 0 1 1 1 0 -1 -1 0 156 0 1 0 -1 1 0 1 0 0 157 0 1 0 -1 1 0 1 1 -1 158 0 1 0 0 0 1 -1 -1 1 159 0 1 0 1 -1 0 2 1 -1 160 0 2 0 -1 1 0 1 2 -2 161 0 2 1 0 -1 1 -1 -2 1 162 1 -7 1 5 5 9 1 1 -3 163 1 -3 -1 3 3 1 1 -1 1 164 1 -3 1 1 1 1 1 1 1 165 1 -3 1 1 5 -3 1 1 5 166 1 -3 1 5 1 1 1 -3 1 167 1 -3 1 5 5 1 -3 -3 1 168 1 -3 5 -1 3 1 -1 3 1 169 1 -3 5 9 13 1 -11 -7 1 170 1 -1 -1 1 1 1 1 -1 1 171 1 -1 0 1 1 0 0 -1 0 172 1 -1 1 1 1 1 -1 -1 -1 173 1 -1 1 3 -1 1 1 -1 -1 174 1 -1 3 0 2 1 -2 0 -1 175 1 -1 3 3 5 1 -5 -3 -1 176 1 0 0 -1 2 -1 1 0 0 177 1 0 0 0 0 0 0 -1 0 178 1 0 0 0 1 -1 0 0 0 179 1 1 -3 1 1 1 1 1 1 180 1 1 -3 1 1 1 1 5 -3 181 1 1 -3 1 1 5 1 -3 5 182 1 1 -3 5 5 -3 -3 5 1 183 1 1 -1 -1 1 1 1 -1 1 184 1 1 -1 1 1 -1 -1 1 1 185 1 1 1 -3 1 1 1 1 1 186 1 1 1 -3 3 -1 3 1 -1 187 1 1 1 -3 5 -3 5 1 1 188 1 1 1 -1 -1 1 -1 -1 1 189 1 1 1 -1 1 -1 1 -1 -1 190 1 1 1 1 -3 1 1 -3 1 191 1 1 1 1 -1 -1 3 -1 -1 192 1 1 1 1 1 -3 1 1 1 193 1 1 1 1 1 1 -3 -3 1 194 1 1 5 1 1 -3 1 -3 1 195 1 2 0 -3 2 1 1 0 -1 196 1 2 1 -1 -1 3 -2 -2 0 197 1 3 -1 -3 3 1 1 -1 1 198 1 3 1 -5 5 -1 5 1 -3 199 1 3 1 -1 -1 1 -1 -3 1 200 1 3 1 -1 -1 3 -3 -3 1 201 1 5 -3 -3 5 1 1 9 -7 202 1 5 1 -7 5 1 5 1 -3 203 1 5 1 -7 9 -3 9 1 -3 204 1 5 3 -3 -1 7 -5 -3 -1 205 2 -1 0 1 1 0 0 -1 -1 206 2 1 0 -3 4 -1 2 0 -2 207 3 -5 -1 3 3 3 3 -1 -1 208 3 -5 3 7 -1 3 3 -5 -1 209 3 -1 -1 -1 3 -1 3 -1 -1 210 3 -1 -1 -1 7 -5 3 3 3 211 3 -1 -1 3 3 -1 -1 -1 -1 212 3 -1 3 -1 3 -1 -1 -1 -1 213 3 -1 3 3 7 -1 -5 -5 -1 214 3 1 1 -1 1 -1 -1 -3 1 215 3 3 -1 -5 3 3 3 -1 -1 216 3 3 -1 -1 -1 3 -1 -5 3 217 3 3 1 -1 -1 1 -3 -5 3 218 3 3 3 -1 -1 -1 -1 -5 3 219 3 7 3 -5 -1 3 -1 -5 -1 220 3 7 3 -1 -5 3 -5 -9 7 221 3 11 3 -1 -5 7 -9 -13 7 222 5 1 1 -7 9 -3 5 1 -3 223 5 1 1 -3 5 -3 1 -3 -3 224 5 5 1 -3 -3 5 -3 -7 1 225 5 9 1 -3 -3 5 -7 -11 5 226 7 -1 3 -1 7 -5 -1 -5 -1 227 7 3 -1 -9 15 -5 7 -1 -5 228 7 11 3 -9 -1 7 -5 -9 -1 229 9 -7 1 5 5 1 1 -7 -3 230 9 -3 1 1 5 -3 1 -7 -3 231 11 -1 -1 -1 7 -5 3 -5 -5 232 2331 congruences: 234 1 1 1 1 1 1 1 1 1 4 235 2369 basis elements of generated lattice: 237 1 0 0 0 0 0 0 0 -1 238 0 1 0 0 0 0 0 0 -1 239 0 0 1 0 0 0 0 0 -1 240 0 0 0 1 0 0 0 0 -1 241 0 0 0 0 1 0 0 0 -1 242 0 0 0 0 0 1 0 0 -1 243 0 0 0 0 0 0 1 0 -1 244 0 0 0 0 0 0 0 1 -1 245 0 0 0 0 0 0 0 0 4 246 247