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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 vertices of polyhedron
4 extreme rays of recession cone
7 support hyperplanes of polyhedron (homogenized)

embedding dimension = 4
affine dimension of the polyhedron = 3 (maximal)
rank of recession monoid = 3
internal index = 2

dehomogenization:
0 0 0 1 

grading:
0 0 1 0 


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

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

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