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

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5 extreme rays
5 support hyperplanes

embedding dimension = 4
rank = 4 (maximal)
external index = 1
internal index = 1

grading:
1 1 1 -2 

degrees of extreme rays:
1: 5  

ideal is not primary to the ideal generated by the indeterminates

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5 extreme rays:
 0 0 1 0
 0 1 0 0
 0 3 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
 1 1 0 -3