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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
8 support hyperplanes

embedding dimension = 5
rank = 4
external index = 1

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

grading:
0 0 0 0 1 

degrees of extreme rays:
1: 6  

multiplicity = 4

integral  = 27773/29515186701000

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6 extreme rays:
 0 0 1 1 1
 0 1 0 1 1
 0 1 1 0 1
 1 0 0 1 1
 1 0 1 0 1
 1 1 0 0 1

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

1 equations:
 1 1 1 1 -2

4 basis elements of lattice:
 1 0 0 -1 0
 0 1 0 -1 0
 0 0 1 -1 0
 0 0 0  2 1