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20 Hilbert basis elements
8 lattice points in polytope (Hilbert basis elements of degree 1)
20 extreme rays
16 support hyperplanes
embedding dimension = 16
rank = 8
external index = 1
size of triangulation = 48
resulting sum of |det|s = 48
grading:
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0
degrees of extreme rays:
1:8 2:12
multiplicity = 21/2
multiplicity (float) = 10.5
volume (lattice normalized) = 21/2
volume (normalized, float) = 10.5
volume (Euclidean) = 0.188561808316
Hilbert series (HSOP):
1 4 18 36 50 36 18 4 1
denominator with 8 factors:
1:4 2:4
degree of Hilbert Series as rational function = -4
The numerator of the Hilbert series is symmetric.
Hilbert series with cyclotomic denominator:
1 4 18 36 50 36 18 4 1
cyclotomic denominator:
1:8 2:4
Hilbert quasi-polynomial of period 2:
0: 480 1136 1216 784 330 89 14 1
1: 390 1051 1186 779 330 89 14 1
with common denominator = 480
rank of class group = 8
class group is free
***********************************************************************
8 lattice points in polytope (Hilbert basis elements of degree 1):
0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0
0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0
0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0
0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1
0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0
0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1
1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0
1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0
12 further Hilbert basis elements of higher degree:
0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0
0 0 1 1 0 1 1 0 2 0 0 0 0 1 0 1
0 0 2 0 0 1 0 1 1 1 0 0 1 0 0 1
0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0
0 1 0 1 2 0 0 0 0 1 1 0 0 0 1 1
0 2 0 0 1 0 1 0 0 0 1 1 1 0 0 1
1 0 0 1 0 0 1 1 1 0 1 0 0 2 0 0
1 0 0 1 1 1 0 0 0 1 0 1 0 0 2 0
1 0 1 0 0 0 0 2 0 1 1 0 1 1 0 0
1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1
1 1 0 0 0 1 1 0 0 0 0 2 1 0 1 0
1 1 0 0 1 0 1 0 0 1 0 1 0 0 1 1
20 extreme rays:
0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0
0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0
0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0
0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1
0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0
0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1
1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0
1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0
0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0
0 0 1 1 0 1 1 0 2 0 0 0 0 1 0 1
0 0 2 0 0 1 0 1 1 1 0 0 1 0 0 1
0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0
0 1 0 1 2 0 0 0 0 1 1 0 0 0 1 1
0 2 0 0 1 0 1 0 0 0 1 1 1 0 0 1
1 0 0 1 0 0 1 1 1 0 1 0 0 2 0 0
1 0 0 1 1 1 0 0 0 1 0 1 0 0 2 0
1 0 1 0 0 0 0 2 0 1 1 0 1 1 0 0
1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1
1 1 0 0 0 1 1 0 0 0 0 2 1 0 1 0
1 1 0 0 1 0 1 0 0 1 0 1 0 0 1 1
16 support hyperplanes:
0 0 0 -1 1 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 1 0 -1 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 2 -1 -1 1 0 -1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 -1 0 0 0 -1 0 0 0 0 0 0 0
0 1 1 2 -1 -1 0 0 -1 0 0 0 0 0 0 0
1 0 -1 -1 1 1 -1 0 1 0 0 0 0 0 0 0
1 0 0 -1 1 0 -1 0 1 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 -1 -1 -1 0 0 0 0 0 0 0 0 0
8 equations:
1 0 0 0 0 0 0 -1 0 0 0 -1 1 0 0 0
0 1 0 0 0 0 0 -1 0 1 -1 -1 1 1 0 -1
0 0 1 0 0 0 0 1 0 -1 1 1 -2 -1 0 0
0 0 0 1 0 0 0 1 0 0 0 1 -1 -1 -1 0
0 0 0 0 1 0 0 1 0 -1 -1 0 0 0 0 0
0 0 0 0 0 1 0 1 0 0 1 1 -2 -1 -1 0
0 0 0 0 0 0 1 -1 0 1 0 -1 1 0 0 -1
0 0 0 0 0 0 0 0 1 1 1 1 -1 -1 -1 -1
8 basis elements of generated lattice:
1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0
0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0
0 0 1 0 0 0 0 1 0 0 1 0 1 1 -1 0
0 0 0 1 0 0 0 1 0 -1 2 0 1 2 -1 -1
0 0 0 0 1 0 0 -1 0 1 -1 0 -1 -1 1 1
0 0 0 0 0 1 0 -1 0 0 -1 1 0 -1 1 0
0 0 0 0 0 0 1 -1 0 -1 0 1 0 1 -1 0
0 0 0 0 0 0 0 0 1 1 -1 -1 -1 -1 1 1
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