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

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

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

dehomogenization:
0 0 0 1 

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1 vertices of polyhedron:
 1 -1 1 1

3 extreme rays of recession cone:
 0 -1 0 0
 0  0 1 0
 1  0 0 0

4 support hyperplanes of polyhedron (homogenized):
 0 -1 0 -1
 0  0 0  1
 0  0 1 -1
 1  0 0 -1