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11 Hilbert basis elements
10 lattice points in polytope (Hilbert basis elements of degree 1)
10 extreme rays
22 support hyperplanes
embedding dimension = 6
rank = 6 (maximal)
external index = 3
internal index = 1
original monoid is not integrally closed in chosen lattice
size of triangulation = 18
resulting sum of |det|s = 21
grading:
1 1 1 1 1 1
with denominator = 3
degrees of extreme rays:
1:10
Hilbert basis elements are not of degree 1
multiplicity = 21
Hilbert series:
1 4 11 4 1
denominator with 6 factors:
1:6
degree of Hilbert Series as rational function = -2
The numerator of the Hilbert series is symmetric.
Hilbert polynomial:
120 314 375 265 105 21
with common denominator = 120
rank of class group = 16
class group is free
***********************************************************************
10 lattice points in polytope (Hilbert basis elements of degree 1):
0 0 1 1 0 1
0 0 1 1 1 0
0 1 0 0 1 1
0 1 0 1 1 0
0 1 1 0 0 1
1 0 0 0 1 1
1 0 0 1 0 1
1 0 1 0 1 0
1 1 0 1 0 0
1 1 1 0 0 0
1 further Hilbert basis elements of higher degree:
1 1 1 1 1 1
10 extreme rays:
0 0 1 1 0 1
0 0 1 1 1 0
0 1 0 0 1 1
0 1 0 1 1 0
0 1 1 0 0 1
1 0 0 0 1 1
1 0 0 1 0 1
1 0 1 0 1 0
1 1 0 1 0 0
1 1 1 0 0 0
22 support hyperplanes:
-2 1 1 1 1 1
-1 -1 2 2 -1 2
-1 -1 2 2 2 -1
-1 2 -1 -1 2 2
-1 2 -1 2 2 -1
-1 2 2 -1 -1 2
0 0 0 0 0 1
0 0 0 0 1 0
0 0 0 1 0 0
0 0 1 0 0 0
0 1 0 0 0 0
1 -2 1 1 1 1
1 0 0 0 0 0
1 1 -2 1 1 1
1 1 1 -2 1 1
1 1 1 1 -2 1
1 1 1 1 1 -2
2 -1 -1 -1 2 2
2 -1 -1 2 -1 2
2 -1 2 -1 2 -1
2 2 -1 2 -1 -1
2 2 2 -1 -1 -1
1 congruences:
1 1 1 1 1 1 3
6 basis elements of generated lattice:
1 0 0 0 0 -1
0 1 0 0 0 -1
0 0 1 0 0 -1
0 0 0 1 0 -1
0 0 0 0 1 -1
0 0 0 0 0 3
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