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

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20 extreme rays
16 support hyperplanes

embedding dimension = 16
rank = 8

***********************************************************************

20 extreme rays:
 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0
 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0
 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0
 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1
 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0
 0 0 1 1 0 1 1 0 2 0 0 0 0 1 0 1
 0 0 2 0 0 1 0 1 1 1 0 0 1 0 0 1
 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0
 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1
 0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0
 0 1 0 1 2 0 0 0 0 1 1 0 0 0 1 1
 0 2 0 0 1 0 1 0 0 0 1 1 1 0 0 1
 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0
 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0
 1 0 0 1 0 0 1 1 1 0 1 0 0 2 0 0
 1 0 0 1 1 1 0 0 0 1 0 1 0 0 2 0
 1 0 1 0 0 0 0 2 0 1 1 0 1 1 0 0
 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1
 1 1 0 0 0 1 1 0 0 0 0 2 1 0 1 0
 1 1 0 0 1 0 1 0 0 1 0 1 0 0 1 1

16 support hyperplanes:
 0 0  0 -1  1  0  0 0  1 0 0 0 0 0 0 0
 0 0  0  0  0  0  0 0  1 0 0 0 0 0 0 0
 0 0  0  0  0  0  1 0  0 0 0 0 0 0 0 0
 0 0  0  0  0  1  0 0  0 0 0 0 0 0 0 0
 0 0  0  0  0  1  1 0 -1 0 0 0 0 0 0 0
 0 0  0  0  1  0  0 0  0 0 0 0 0 0 0 0
 0 0  0  1  0  0  0 0  0 0 0 0 0 0 0 0
 0 0  1  0  0  0  0 0  0 0 0 0 0 0 0 0
 0 0  1  2 -1 -1  1 0 -1 0 0 0 0 0 0 0
 0 1  0  0  0  0  0 0  0 0 0 0 0 0 0 0
 0 1  1  1 -1  0  0 0 -1 0 0 0 0 0 0 0
 0 1  1  2 -1 -1  0 0 -1 0 0 0 0 0 0 0
 1 0 -1 -1  1  1 -1 0  1 0 0 0 0 0 0 0
 1 0  0 -1  1  0 -1 0  1 0 0 0 0 0 0 0
 1 0  0  0  0  0  0 0  0 0 0 0 0 0 0 0
 1 1  1  1 -1 -1 -1 0  0 0 0 0 0 0 0 0

8 equations:
 1 0 0 0 0 0 0 -1 0  0  0 -1  1  0  0  0
 0 1 0 0 0 0 0 -1 0  1 -1 -1  1  1  0 -1
 0 0 1 0 0 0 0  1 0 -1  1  1 -2 -1  0  0
 0 0 0 1 0 0 0  1 0  0  0  1 -1 -1 -1  0
 0 0 0 0 1 0 0  1 0 -1 -1  0  0  0  0  0
 0 0 0 0 0 1 0  1 0  0  1  1 -2 -1 -1  0
 0 0 0 0 0 0 1 -1 0  1  0 -1  1  0  0 -1
 0 0 0 0 0 0 0  0 1  1  1  1 -1 -1 -1 -1

8 basis elements of lattice:
 1 0 0 0 0 0 0  1 0  1  0  0  0  0  1  0
 0 1 0 0 0 0 0  1 0  0  1  0  1  0  0  0
 0 0 1 0 0 0 0  1 0  0  1  0  1  1 -1  0
 0 0 0 1 0 0 0  1 0 -1  2  0  1  2 -1 -1
 0 0 0 0 1 0 0 -1 0  1 -1  0 -1 -1  1  1
 0 0 0 0 0 1 0 -1 0  0 -1  1  0 -1  1  0
 0 0 0 0 0 0 1 -1 0 -1  0  1  0  1 -1  0
 0 0 0 0 0 0 0  0 1  1 -1 -1 -1 -1  1  1