1155 Hilbert basis elements
20 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 = 1
9internal index = 4
10original monoid is not integrally closed in chosen lattice
11
12size of triangulation   = 281
13resulting sum of |det|s = 1700
14
15grading:
161 1 1 1 1 1 1 1 1
17
18degrees of extreme rays:
194:19
20
21multiplicity = 425/65536
22multiplicity (float) = 0.00648498535156
23
24Hilbert series:
251 -1 0 0 11 -11 6 -4 58 -34 33 -12 150 -30 60 14 117 2 29 16 16 0 3 1
26denominator with 9 factors:
271:1  4:8
28
29degree of Hilbert Series as rational function = -10
30
31Hilbert series with cyclotomic denominator:
32-1 1 0 0 -11 11 -6 4 -58 34 -33 12 -150 30 -60 -14 -117 -2 -29 -16 -16 0 -3 -1
33cyclotomic denominator:
341:9  2:8  4:8
35
36Hilbert quasi-polynomial of period 4:
37 0:  2642411520 2334916608 885112832 195743744 28698880 2949632 225568 13136 425
38 1:    47747385  -21245592 -21642612  -4398408  -543130   33432  41132  7368 425
39 2:   -55883520  -47314944    397056   9730560  3110240  491904  69104  8160 425
40 3:    -6462855  -15019176  -5887796   3363080   543270 -162904  -6804  5240 425
41with common denominator = 2642411520
42
43***********************************************************************
44
450 lattice points in polytope (Hilbert basis elements of degree 1):
46
47155 further Hilbert basis elements of higher degree:
48 0 0 0 0 1 1 1 0 1
49 0 0 1 1 1 1 0 0 0
50 0 1 0 0 1 1 1 0 0
51 0 1 0 1 1 0 0 0 1
52 0 1 0 1 1 1 0 0 0
53 0 1 1 0 1 0 1 0 0
54 0 1 1 0 1 1 0 0 0
55 0 1 1 1 0 0 1 0 0
56 0 1 1 1 1 0 0 0 0
57 1 0 0 1 0 1 1 0 0
58 1 0 0 1 1 1 0 0 0
59 1 0 1 0 0 0 0 1 1
60 1 0 1 0 0 1 0 1 0
61 1 0 1 1 1 0 0 0 0
62 1 1 0 0 0 1 0 0 1
63 1 1 0 0 1 0 1 0 0
64 1 1 0 1 0 0 0 1 0
65 1 1 1 0 1 0 0 0 0
66 1 1 1 1 0 0 0 0 0
67 0 1 1 1 1 1 1 0 0
68 1 1 0 0 1 1 1 0 1
69 1 1 0 1 1 1 0 0 1
70 1 1 0 1 1 1 1 0 0
71 1 1 1 1 1 0 1 0 0
72 1 1 1 1 1 1 0 0 0
73 1 1 0 1 1 1 1 0 1
74 1 1 1 1 1 1 1 0 0
75 1 1 0 1 1 2 1 0 1
76 1 1 0 1 2 1 1 0 1
77 2 1 1 1 1 1 0 1 0
78 0 2 1 1 2 1 1 0 1
79 0 2 1 1 2 2 1 0 0
80 0 2 2 1 2 1 1 0 0
81 1 1 0 1 2 2 1 0 1
82 1 1 1 1 1 1 1 1 1
83 1 1 1 1 2 1 1 0 1
84 1 1 1 2 2 1 0 0 1
85 1 1 1 2 2 2 0 0 0
86 1 1 2 2 2 1 0 0 0
87 1 2 0 1 2 1 1 0 1
88 1 2 1 1 1 1 1 0 1
89 1 2 1 1 1 1 1 1 0
90 1 2 1 1 2 1 0 0 1
91 1 2 1 1 2 1 1 0 0
92 1 2 1 2 1 1 1 0 0
93 1 2 2 1 2 0 1 0 0
94 1 2 2 1 2 1 0 0 0
95 1 2 2 2 1 0 1 0 0
96 2 1 0 1 1 2 1 0 1
97 2 1 1 0 1 1 1 1 1
98 2 1 1 1 1 1 0 1 1
99 2 1 1 2 1 1 0 1 0
100 2 1 1 2 1 1 1 0 0
101 2 1 2 1 1 0 0 1 1
102 2 1 2 1 1 1 0 1 0
103 2 2 1 1 1 1 0 0 1
104 0 2 1 1 2 1 2 0 1
105 1 1 0 2 2 2 1 0 1
106 1 1 1 2 2 1 1 0 1
107 1 2 2 1 1 1 1 1 0
108 2 0 1 1 1 2 1 1 1
109 2 1 2 2 1 1 0 1 0
110 2 2 1 1 1 1 0 1 1
111 2 2 1 1 1 1 1 1 0
112 2 2 2 1 1 1 0 1 0
113 0 2 2 2 2 2 1 0 0
114 1 2 0 1 2 2 1 0 2
115 1 2 1 2 2 2 0 0 1
116 1 2 2 2 1 1 1 1 0
117 1 2 2 2 2 2 0 0 0
118 2 1 0 1 2 2 2 0 1
119 2 1 1 0 1 2 1 1 2
120 2 1 1 2 1 1 1 1 1
121 2 1 1 2 1 2 1 1 0
122 2 1 1 2 2 2 0 0 1
123 2 1 2 1 1 2 0 1 1
124 2 2 0 1 2 2 1 0 1
125 2 2 1 1 1 1 0 1 2
126 2 2 1 1 1 1 1 1 1
127 2 2 1 1 1 2 0 1 1
128 2 2 1 1 2 2 0 0 1
129 2 2 1 2 1 1 0 1 1
130 2 2 1 2 1 1 2 0 0
131 2 2 1 2 2 1 0 0 1
132 2 2 1 2 2 1 1 0 0
133 2 2 2 1 1 1 0 1 1
134 2 2 2 1 1 1 1 1 0
135 2 2 2 2 1 0 0 1 1
136 2 2 2 2 1 1 0 1 0
137 2 2 2 2 2 0 1 0 0
138 2 2 2 2 2 1 0 0 0
139 1 3 1 1 2 1 2 0 1
140 2 2 1 1 1 1 1 1 2
141 2 2 1 1 1 2 1 1 1
142 2 2 2 2 1 0 1 1 1
143 2 2 2 2 2 0 0 1 1
144 3 1 1 1 1 2 1 1 1
145 3 2 1 1 1 1 1 1 1
146 3 2 2 1 1 1 0 1 1
147 1 1 1 2 2 3 2 0 1
148 1 2 1 1 2 2 3 0 1
149 1 2 1 1 2 3 2 0 1
150 1 2 1 2 2 2 1 0 2
151 1 2 1 2 2 3 1 0 1
152 1 2 1 3 2 2 1 0 1
153 2 1 2 2 1 2 1 1 1
154 2 2 1 2 1 1 1 1 2
155 2 2 1 2 1 1 2 1 1
156 2 2 1 2 1 2 1 1 1
157 2 2 1 3 1 1 1 1 1
158 2 2 1 3 1 2 1 1 0
159 2 2 2 2 1 1 2 1 0
160 2 2 2 2 2 0 1 1 1
161 2 3 1 2 2 0 1 1 1
162 3 2 1 1 1 2 1 1 1
163 3 2 1 2 1 1 1 1 1
164 3 2 2 1 1 1 0 2 1
165 3 2 2 2 1 1 1 1 0
166 2 2 1 1 2 1 2 1 2
167 2 2 1 2 1 2 2 1 1
168 2 2 2 3 1 1 1 1 1
169 2 2 2 3 1 2 1 1 0
170 2 3 1 2 1 1 1 1 2
171 2 3 2 2 2 0 1 1 1
172 2 3 2 3 1 0 1 1 1
173 2 3 2 3 2 0 0 1 1
174 3 2 2 2 2 0 1 1 1
175 3 2 2 3 1 1 1 1 0
176 3 2 3 2 2 0 0 1 1
177 0 3 2 1 3 2 3 0 1
178 1 2 1 2 2 3 3 0 1
179 1 2 2 2 2 3 2 0 1
180 1 2 3 1 2 2 2 1 1
181 1 3 1 2 2 3 2 0 1
182 1 3 2 2 2 1 2 1 1
183 1 3 3 1 2 2 2 1 0
184 1 3 3 2 2 1 1 1 1
185 2 2 3 3 1 1 1 1 1
186 2 2 3 3 1 2 1 1 0
187 2 3 1 1 2 2 3 0 1
188 2 3 1 2 1 2 2 1 1
189 2 3 2 2 2 0 2 1 1
190 2 3 2 3 2 0 1 1 1
191 3 1 1 2 2 2 2 1 1
192 3 1 3 3 2 2 0 1 0
193 3 2 2 2 2 1 2 1 0
194 3 2 3 3 1 1 1 1 0
195 2 3 1 2 2 1 2 1 2
196 3 3 2 3 2 0 1 1 1
197 3 3 3 3 3 0 0 1 1
198 4 1 2 2 2 2 1 2 1
199 4 3 1 2 1 2 2 1 1
200 4 3 2 2 1 2 2 1 1
201 3 4 3 4 3 0 0 1 1
202 4 3 2 2 1 2 2 2 1
203
20419 extreme rays:
205 0 0 0 0 1 1 1 0 1
206 0 0 1 1 1 1 0 0 0
207 0 1 0 0 1 1 1 0 0
208 0 1 0 1 1 0 0 0 1
209 0 1 0 1 1 1 0 0 0
210 0 1 1 0 1 0 1 0 0
211 0 1 1 0 1 1 0 0 0
212 0 1 1 1 0 0 1 0 0
213 0 1 1 1 1 0 0 0 0
214 1 0 0 1 0 1 1 0 0
215 1 0 0 1 1 1 0 0 0
216 1 0 1 0 0 0 0 1 1
217 1 0 1 0 0 1 0 1 0
218 1 0 1 1 1 0 0 0 0
219 1 1 0 0 0 1 0 0 1
220 1 1 0 0 1 0 1 0 0
221 1 1 0 1 0 0 0 1 0
222 1 1 1 0 1 0 0 0 0
223 1 1 1 1 0 0 0 0 0
224
225134 support hyperplanes:
226 -11  5  9 -3  5 13   1   9  -7
227  -7 -3  1  9 17  5  -7   1   5
228  -7  1  5  1  1  9   5   5  -3
229  -7  1  9 -3 13 17  -7   9 -11
230  -5  3  5 -1  1  5   1   3  -3
231  -3  1 -3  5  5  1  -3   5   1
232  -3  1  1  1  1  1   1   1   1
233  -3  1  3 -1  1  3   1   3  -1
234  -3  1  3  1 -1  3   3   1  -1
235  -3  3 -1  1  3  5  -3  -1   5
236  -3  5 -3  5  1 -3   1   9   1
237  -3  5 -3  5  1  1  -3   5   1
238  -1 -5 -1  7  7  3  -1  -1   3
239  -1 -3  1  3  5 -1  -1   1   5
240  -1 -1 -1  3  3 -1  -1   3   3
241  -1 -1  1  1  1 -1   1   1   3
242  -1 -1  2  0  0  1   2   2   1
243  -1 -1  3 -1 -1  3   3   3   3
244  -1 -1  3 -1  1  1   1   3   1
245  -1  0  1  0  0  1   1   1   0
246  -1  1 -1  1  1 -1   1   3   1
247  -1  1 -1  1  1  1  -1   1   1
248  -1  1 -1  1  1  1  -1   3  -1
249  -1  1 -1  1  1  3  -1  -1   3
250  -1  1 -1  1  1  3  -1   5  -3
251  -1  1 -1  2  1  0  -1   2   0
252  -1  1 -1  3  1 -1  -1   3   1
253  -1  1  0  0  1  2  -1   3  -2
254  -1  1  0  1  0  0   0   1   0
255  -1  1  0  2  0 -1   0   2   1
256  -1  1  1 -1  1  1   1   1  -1
257  -1  1  1 -1  1  3  -1   1  -1
258  -1  1  1  0  0  1   0   1  -1
259  -1  1  1  1 -1  1   1   1  -1
260  -1  1  2  0  0  1   0   0  -1
261  -1  1  2  1  0  0   0  -1   0
262  -1  1  4  2  0 -1   0  -2   1
263  -1  3 -5  3  3 -1  -1   7  -1
264  -1  3 -1 -1  3 -1   3   3  -1
265  -1  3 -1  1  1 -1   1   3  -1
266  -1  3 -1  3 -1 -1  -1   3   3
267  -1  3 -1  3 -1 -1   3   3  -1
268  -1  3  3 -1 -1  3  -1  -1  -1
269   0 -2  3 -1  2  1   0   3   1
270   0 -1  0  1  1  0   0   0   1
271   0 -1  1  0  1  0   0   1   1
272   0  0  0  0  0  0   0   0   1
273   0  0  0  0  0  0   0   1   0
274   0  0  0  0  0  0   1   0   0
275   0  0  0  0  0  1   0   0   0
276   0  0  0  0  1 -1   1   1   1
277   0  0  0  1  0  0   0   0   0
278   0  0  0  1  1  0  -1   0   0
279   0  0  1 -1  0  1   0   1   1
280   0  0  1  0  0  0   0   0   0
281   0  0  1  0  1  1  -1   0  -1
282   0  0  1  1 -1  0   1  -1   0
283   0  0  1  1  1  0  -1  -1   0
284   0  1  0 -1  1  0   1   0   0
285   0  1  0 -1  1  0   1   1  -1
286   0  1  0  0  0  1  -1  -1   1
287   0  1  0  1 -1  0   2   1  -1
288   0  2  0 -1  1  0   1   2  -2
289   0  2  1  0 -1  1  -1  -2   1
290   1 -7  1  5  5  9   1   1  -3
291   1 -3 -1  3  3  1   1  -1   1
292   1 -3  1  1  1  1   1   1   1
293   1 -3  1  1  5 -3   1   1   5
294   1 -3  1  5  1  1   1  -3   1
295   1 -3  1  5  5  1  -3  -3   1
296   1 -3  5 -1  3  1  -1   3   1
297   1 -3  5  9 13  1 -11  -7   1
298   1 -1 -1  1  1  1   1  -1   1
299   1 -1  0  1  1  0   0  -1   0
300   1 -1  1  1  1  1  -1  -1  -1
301   1 -1  1  3 -1  1   1  -1  -1
302   1 -1  3  0  2  1  -2   0  -1
303   1 -1  3  3  5  1  -5  -3  -1
304   1  0  0 -1  2 -1   1   0   0
305   1  0  0  0  0  0   0  -1   0
306   1  0  0  0  1 -1   0   0   0
307   1  1 -3  1  1  1   1   1   1
308   1  1 -3  1  1  1   1   5  -3
309   1  1 -3  1  1  5   1  -3   5
310   1  1 -3  5  5 -3  -3   5   1
311   1  1 -1 -1  1  1   1  -1   1
312   1  1 -1  1  1 -1  -1   1   1
313   1  1  1 -3  1  1   1   1   1
314   1  1  1 -3  3 -1   3   1  -1
315   1  1  1 -3  5 -3   5   1   1
316   1  1  1 -1 -1  1  -1  -1   1
317   1  1  1 -1  1 -1   1  -1  -1
318   1  1  1  1 -3  1   1  -3   1
319   1  1  1  1 -1 -1   3  -1  -1
320   1  1  1  1  1 -3   1   1   1
321   1  1  1  1  1  1  -3  -3   1
322   1  1  5  1  1 -3   1  -3   1
323   1  2  0 -3  2  1   1   0  -1
324   1  2  1 -1 -1  3  -2  -2   0
325   1  3 -1 -3  3  1   1  -1   1
326   1  3  1 -5  5 -1   5   1  -3
327   1  3  1 -1 -1  1  -1  -3   1
328   1  3  1 -1 -1  3  -3  -3   1
329   1  5 -3 -3  5  1   1   9  -7
330   1  5  1 -7  5  1   5   1  -3
331   1  5  1 -7  9 -3   9   1  -3
332   1  5  3 -3 -1  7  -5  -3  -1
333   2 -1  0  1  1  0   0  -1  -1
334   2  1  0 -3  4 -1   2   0  -2
335   3 -5 -1  3  3  3   3  -1  -1
336   3 -5  3  7 -1  3   3  -5  -1
337   3 -1 -1 -1  3 -1   3  -1  -1
338   3 -1 -1 -1  7 -5   3   3   3
339   3 -1 -1  3  3 -1  -1  -1  -1
340   3 -1  3 -1  3 -1  -1  -1  -1
341   3 -1  3  3  7 -1  -5  -5  -1
342   3  1  1 -1  1 -1  -1  -3   1
343   3  3 -1 -5  3  3   3  -1  -1
344   3  3 -1 -1 -1  3  -1  -5   3
345   3  3  1 -1 -1  1  -3  -5   3
346   3  3  3 -1 -1 -1  -1  -5   3
347   3  7  3 -5 -1  3  -1  -5  -1
348   3  7  3 -1 -5  3  -5  -9   7
349   3 11  3 -1 -5  7  -9 -13   7
350   5  1  1 -7  9 -3   5   1  -3
351   5  1  1 -3  5 -3   1  -3  -3
352   5  5  1 -3 -3  5  -3  -7   1
353   5  9  1 -3 -3  5  -7 -11   5
354   7 -1  3 -1  7 -5  -1  -5  -1
355   7  3 -1 -9 15 -5   7  -1  -5
356   7 11  3 -9 -1  7  -5  -9  -1
357   9 -7  1  5  5  1   1  -7  -3
358   9 -3  1  1  5 -3   1  -7  -3
359  11 -1 -1 -1  7 -5   3  -5  -5
360
361