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

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

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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 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

