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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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6 extreme rays
7 support hyperplanes

embedding dimension = 6
rank = 5
external index = 1
internal index = 1
original monoid is not integrally closed
witness for not being integrally closed:
8 2 8 4 1 1 

grading:
0 0 0 0 0 1 

degrees of extreme rays:
1: 6  

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

6 extreme rays:
  4 7  3 5 4 1
  8 3  7 5 0 1
  9 0 10 3 1 1
  9 0 10 4 0 1
 10 0  9 4 0 1
 11 0  7 5 0 1

7 support hyperplanes:
 -3 -4 -3  0 0   57
 -1 -1 -1 -1 0   23
 -1 -1  0  1 0    6
  0 -1 -1  0 0   10
  0  1  0  0 0    0
  1  1  0 -2 0   -1
 21 29 14  0 0 -329

1 equations:
 1 1 1 1 1 -23

5 basis elements of lattice:
 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 23 1