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

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3 module generators
4 Hilbert basis elements of recession monoid
2 vertices of polyhedron
4 extreme rays of recession cone
5 support hyperplanes of polyhedron (homogenized)

embedding dimension = 4
affine dimension of the polyhedron = 3 (maximal)
rank of recession monoid = 3

size of partial triangulation   = 1
resulting sum of |det|s = 2

dehomogenization:
0 0 0 1 

grading:
0 0 1 0 


module rank = 1

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3 module generators:
 2 0 2 1
 2 1 2 1
 2 2 2 1

4 Hilbert basis elements of recession monoid:
 0 0 1 0
 0 1 1 0
 1 0 1 0
 1 1 1 0

2 vertices of polyhedron:
 2 0 2 1
 2 2 2 1

4 extreme rays of recession cone:
 0 0 1 0
 0 1 1 0
 1 0 1 0
 1 1 1 0

5 support hyperplanes of polyhedron (homogenized):
 -1  0 1  0
  0 -1 1  0
  0  0 0  1
  0  1 0  0
  1  0 0 -2