12 Hilbert basis elements
6 lattice points in polytope (Hilbert basis elements of degree 1)
7 extreme rays
8 support hyperplanes

embedding dimension = 5
rank = 5 (maximal)
external index = 1
internal index = 2
original monoid is not integrally closed

size of triangulation   = 4
resulting sum of |det|s = 14

grading:
0 0 0 0 1 

degrees of extreme rays:
1: 5  2: 1  3: 1  

multiplicity = 10/3
multiplicity (float) = 3.33333333333

Hilbert series:
1 2 4 3 4 2 4 
denominator with 5 factors:
1: 4  6: 1  

degree of Hilbert Series as rational function = -4

Hilbert series with cyclotomic denominator:
-1 -3 -6 -6 -4 
cyclotomic denominator:
1: 5  2: 1  3: 1  

Hilbert quasi-polynomial of period 6:
 0:  72 150 139 62 10
 1:  71 150 139 62 10
 2:  72 150 139 62 10
 3:  63 150 139 62 10
 4:  80 150 139 62 10
 5:  63 150 139 62 10
with common denominator = 72

rank of class group = 3
finite cyclic summands:
2: 1  

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6 lattice points in polytope (Hilbert basis elements of degree 1):
 0 1 1 0 1
 0 2 0 0 1
 2 0 1 0 1
 2 1 0 0 1
 3 1 0 0 1
 4 0 0 0 1

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

7 extreme rays:
         0          1          1          0          1 
         0          2          0          0          1 
         2          0          1          0          1 
         3          1          0          0          1 
         4          0          0          0          1 
         0          2        0.5          0          1 
         0          0          0   0.666667          1 

8 support hyperplanes:
 -0.214286  -0.357143  -0.571429       -1.5          1 
 -0.166667       -0.5          0       -1.5          1 
 -0.166667  -0.333333  -0.666667       -1.5          1 
     -0.25      -0.25       -0.5       -1.5          1 
         0          0          0          1          0 
         0          0          1          0          0 
         1          0          0          0          0 
      0.25        0.5        0.5        1.5         -1 

