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

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4 extreme rays
4 support hyperplanes

embedding dimension = 9
rank = 3

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4 extreme rays:
 0 2 1 2 1 0 1 0 2
 1 0 2 2 1 0 0 2 1
 1 2 0 0 1 2 2 0 1
 2 0 1 0 1 2 1 2 0

4 support hyperplanes:
 -2  1  4 0 0 0 0 0 0
  0  1  0 0 0 0 0 0 0
  2 -1  2 0 0 0 0 0 0
  4  1 -2 0 0 0 0 0 0

6 equations:
 3 0 0 0 0 0 -2 -2  1
 0 3 0 0 0 0 -2  1 -2
 0 0 3 0 0 0  1 -2 -2
 0 0 0 3 0 0  2 -1 -4
 0 0 0 0 3 0 -1 -1 -1
 0 0 0 0 0 3 -4 -1  2

3 basis elements of lattice:
 3 0 0 -2 1  4  2  2 -1
 0 3 0  1 1  1  2 -1  2
 0 0 3  4 1 -2 -1  2  2