8 Hilbert basis elements
1 Hilbert basis elements of degree 1
3 extreme rays
3 support hyperplanes

embedding dimension = 3
rank = 3 (maximal)
index = 15
original monoid is not integrally closed

size of triangulation   = 1
resulting sum of |det|s = 15

grading:
0 0 1 

degrees of extreme rays:
2: 1  3: 1  4: 1  

multiplicity = 5/8

Hilbert series:
1 0 0 3 2 -1 2 2 1 1 1 1 2 
denominator with 3 factors:
1: 1  2: 1  12: 1  

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

Hilbert quasi-polynomial of period 12:
  0:   48  28  15
  1:   11  22  15
  2:  -20  28  15
  3:   39  22  15
  4:   32  28  15
  5:   -5  22  15
  6:   12  28  15
  7:   23  22  15
  8:   16  28  15
  9:   27  22  15
 10:   -4  28  15
 11:    7  22  15
with common denominator = 48

***********************************************************************

8 Hilbert basis elements:
 -1 -1  3
  0 -2  5
  0 -1  3
  0  0  1
  1 -2  4
  1 -1  4
  1  0  3
  1  1  2

3 extreme rays:
  1  1  2
 -1 -1  3
  1 -2  4

3 support hyperplanes:
  2  7  3
 -8  2  3
  1 -1  0

1 Hilbert basis elements of degree 1:
 0 0 1

