3x3magiceven.ref

9 Hilbert basis elements
0 Hilbert basis elements of degree 1
4 extreme rays
4 support hyperplanes

embedding dimension = 9
rank = 3
external index = 4

size of triangulation   = 2
resulting sum of |det|s = 8

grading:
1 1 1 0 0 0 0 0 0 
with denominator = 3

degrees of extreme rays:
2: 4  

multiplicity = 1

Hilbert series:
1 -1 3 1 
denominator with 3 factors:
1: 1  2: 2  

degree of Hilbert Series as rational function = -2

Hilbert series with cyclotomic denominator:
-1 1 -3 -1 
cyclotomic denominator:
1: 3  2: 2  

Hilbert quasi-polynomial of period 2:
 0:   2 2 1
 1:  -1 0 1
with common denominator = 2

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0 Hilbert basis elements of degree 1:

9 further Hilbert basis elements of higher degree:
 0 4 2 4 2 0 2 0 4
 2 0 4 4 2 0 0 4 2
 2 2 2 2 2 2 2 2 2
 2 4 0 0 2 4 4 0 2
 4 0 2 0 2 4 2 4 0
 2 3 4 5 3 1 2 3 4
 2 5 2 3 3 3 4 1 4
 4 1 4 3 3 3 2 5 2
 4 3 2 1 3 5 4 3 2

4 extreme rays:
 0 4 2 4 2 0 2 0 4
 2 0 4 4 2 0 0 4 2
 2 4 0 0 2 4 4 0 2
 4 0 2 0 2 4 2 4 0

4 support hyperplanes:
 0 -1 0 0 0 0  2 0 0
 0  1 0 0 0 0  0 0 0
 2  1 0 0 0 0 -2 0 0
 2  3 0 0 0 0 -4 0 0

6 equations:
 1 0 0 0 0  1 -2 -1  1
 0 1 0 0 0  1 -2  0  0
 0 0 1 0 0  1 -1 -1  0
 0 0 0 1 0 -1  2  0 -2
 0 0 0 0 1 -1  1  0 -1
 0 0 0 0 0  3 -4 -1  2

2 congruences:
 1 0 0 0 0 0 0 0 0 2
 0 1 0 0 1 0 0 0 0 2

3 basis elements of lattice:
 2 0 -2 -4 0  4  2 0 -2
 0 1  2  3 1 -1  0 1  2
 0 0  6  8 2 -4 -2 4  4