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

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14 Hilbert basis elements
14 extreme rays
34 support hyperplanes

embedding dimension = 9
rank = 9 (maximal)
external index = 1
internal index = 1
original monoid is integrally closed

size of partial triangulation   = 1
resulting sum of |det|s = 2

No implicit grading found

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14 Hilbert basis elements:
 0 0 0 0 0 0 0 1 0
 0 0 0 0 0 0 1 0 0
 0 0 0 0 0 1 0 0 0
 0 0 0 0 1 0 0 0 0
 0 0 0 0 1 1 1 1 1
 0 0 0 1 0 0 0 0 0
 0 0 1 0 0 0 0 0 0
 0 0 1 1 0 1 0 1 1
 0 1 0 0 0 0 0 0 0
 0 1 0 0 0 0 1 1 1
 1 0 0 0 0 0 0 0 0
 1 0 1 0 0 0 1 0 1
 1 1 0 1 1 0 0 0 1
 1 1 1 1 0 0 0 0 1

14 extreme rays:
 0 0 0 0 0 0 0 1 0
 0 0 0 0 0 0 1 0 0
 0 0 0 0 0 1 0 0 0
 0 0 0 0 1 0 0 0 0
 0 0 0 0 1 1 1 1 1
 0 0 0 1 0 0 0 0 0
 0 0 1 0 0 0 0 0 0
 0 0 1 1 0 1 0 1 1
 0 1 0 0 0 0 0 0 0
 0 1 0 0 0 0 1 1 1
 1 0 0 0 0 0 0 0 0
 1 0 1 0 0 0 1 0 1
 1 1 0 1 1 0 0 0 1
 1 1 1 1 0 0 0 0 1

34 support hyperplanes:
 0 0 0 0 0 0 0 0  1
 0 0 0 0 0 0 0 1  0
 0 0 0 0 0 0 1 0  0
 0 0 0 0 0 1 0 0  0
 0 0 0 0 1 0 0 0  0
 0 0 0 1 0 0 0 0  0
 0 0 0 1 0 0 1 0 -1
 0 0 1 0 0 0 0 0  0
 0 0 1 0 1 0 0 1 -1
 0 0 1 0 1 0 1 0 -1
 0 0 1 1 0 0 0 1 -1
 0 1 0 0 0 0 0 0  0
 0 1 0 0 0 0 1 1 -1
 0 1 0 0 0 1 1 0 -1
 0 1 1 0 0 0 0 1 -1
 0 1 1 0 0 0 1 0 -1
 0 1 1 0 0 1 0 0 -1
 0 1 1 0 1 0 0 0 -1
 0 1 1 0 1 1 1 0 -2
 0 1 2 0 1 0 0 1 -2
 0 1 2 0 1 0 1 0 -2
 0 1 2 0 2 0 1 1 -3
 0 2 1 0 0 0 1 1 -2
 0 2 1 0 0 1 1 0 -2
 0 2 2 0 1 1 1 0 -3
 0 2 3 0 2 0 1 1 -4
 1 0 0 0 0 0 0 0  0
 1 0 0 0 0 0 0 1 -1
 1 0 0 0 0 1 1 0 -1
 1 0 1 0 0 0 1 0 -1
 1 1 0 0 0 1 0 0 -1
 1 1 0 0 0 2 1 0 -2
 1 1 0 1 1 0 0 0 -1
 1 2 1 0 0 2 1 0 -3