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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
5 support hyperplanes

embedding dimension = 4
rank = 4 (maximal)
external index = 1
internal index = 1
original monoid is not integrally closed
witness for not being integrally closed:
2 2 0 1 


ideal is primary to the ideal generated by the indeterminates

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6 extreme rays:
 0 0 1 0
 0 0 1 1
 0 1 0 0
 0 5 0 1
 1 0 0 0
 3 0 0 1

5 support hyperplanes:
 0 0  0   1
 0 0  1   0
 0 1  0   0
 1 0  0   0
 5 3 15 -15