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17 Hilbert basis elements
1 lattice points in polytope (Hilbert basis elements of degree 1)
16 extreme rays
11 support hyperplanes
3 excluded faces
embedding dimension = 8
rank = 8 (maximal)
external index = 1
size of triangulation = 16
resulting sum of |det|s = 19
grading:
1 1 1 1 1 1 1 1
degrees of extreme rays:
1:1 2:13 4:2
multiplicity = 1/8
multiplicity (float) = 0.125
Hilbert series:
1 0 8 0 14 1 7 0 1
denominator with 8 factors:
1:1 2:6 4:1
shift = 1
degree of Hilbert Series as rational function = -8
Expansion of Hilbert series
1: 1
2: 1
3: 15
4: 15
5: 99
6: 100
7: 429
8: 435
9: 1430
10: 1452
11: 3978
12: 4040
13: 9690
14: 9838
15: 21318
16: 21632
17: 43263
18: 43873
19: 82225
20: 83331
21: 148005
22: 149902
23: 254475
24: 257583
25: 420732
26: 425632
27: 672452
28: 679928
29: 1043460
30: 1054548
31: 1577532
32: 1593576
33: 2330445
34: 2353161
35: 3372291
36: 3403839
37: 4790071
38: 4833136
39: 6690585
40: 6748467
41: 9203634
42: 9280348
43: 12485550
44: 12585936
45: 16723070
46: 16852914
47: 22137570
48: 22303736
49: 28989675
50: 29200249
51: 37584261
Hilbert series with cyclotomic denominator:
1 0 8 0 14 1 7 0 1
cyclotomic denominator:
1:8 2:7 4:1
Hilbert quasi-polynomial of period 4:
0: 0 16896 25312 24304 11830 2884 343 16
1: 80640 209088 210112 108304 31360 5152 448 16
2: 10080 16896 25312 24304 11830 2884 343 16
3: 80640 209088 210112 108304 31360 5152 448 16
with common denominator = 645120
rank of class group = 3
class group is free
***********************************************************************
1 lattice points in polytope (Hilbert basis elements of degree 1):
1 0 0 0 0 0 0 0
16 further Hilbert basis elements of higher degree:
0 0 0 1 0 0 1 0
0 0 1 0 0 1 0 0
0 0 1 1 0 0 0 0
0 1 0 0 1 0 0 0
0 1 0 1 0 0 0 0
0 1 1 0 0 0 0 0
1 0 0 0 0 0 0 1
1 0 0 0 0 0 1 0
1 0 0 0 0 1 0 0
1 0 0 0 1 0 0 0
1 0 0 1 0 0 0 0
1 0 1 0 0 0 0 0
1 1 0 0 0 0 0 0
0 1 1 1 0 0 0 0
0 1 1 1 0 0 0 1
1 0 0 0 1 1 1 0
16 extreme rays:
1 0 0 0 0 0 0 0
0 0 0 1 0 0 1 0
0 0 1 0 0 1 0 0
0 0 1 1 0 0 0 0
0 1 0 0 1 0 0 0
0 1 0 1 0 0 0 0
0 1 1 0 0 0 0 0
1 0 0 0 0 0 0 1
1 0 0 0 0 0 1 0
1 0 0 0 0 1 0 0
1 0 0 0 1 0 0 0
1 0 0 1 0 0 0 0
1 0 1 0 0 0 0 0
1 1 0 0 0 0 0 0
0 1 1 1 0 0 0 1
1 0 0 0 1 1 1 0
11 support hyperplanes:
0 0 0 0 0 0 0 1
0 0 0 0 0 0 1 0
0 0 0 0 0 1 0 0
0 0 0 0 1 0 0 0
0 0 0 1 0 0 0 0
0 0 1 0 0 0 0 0
0 1 0 0 0 0 0 0
1 -1 1 1 1 -1 -1 -1
1 0 0 0 0 0 0 0
1 1 -1 1 -1 1 -1 -1
1 1 1 -1 -1 -1 1 -1
3 excluded faces:
1 -1 1 1 1 -1 -1 -1
1 1 -1 1 -1 1 -1 -1
1 1 1 -1 -1 -1 1 -1
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