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

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190 extreme rays
32 support hyperplanes

embedding dimension = 6
rank = 6 (maximal)

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

190 extreme rays:
  0  0  0  1  6 1
  0  0  0  1 21 1
  0  0  0  2 21 1
  0  0  0 16  6 1
  0  0  0 16  7 1
  0  0  1 17  5 1
  0  0  2 17  4 1
  0  0  3  1 18 1
  0  0  3  2 18 1
  0  0  4  1  2 1
  0  0  4 15  2 1
  0  0  4 16  3 1
  0  0  5 15  2 1
  0  0  9  1  6 1
  0  0 10  1  2 1
  0  0 10  1  3 1
  0  0 10  2  4 1
  0  0 10  9  4 1
  0  0 10 10  2 1
  0  0 10 10  3 1
  0  1  0  1 21 1
  0  1  0 17  5 1
  0  1  1  1 20 1
  0  1  4 16  2 1
  0  1  9 11  2 1
  0  2  0  1  4 1
  0  2  0  1 20 1
  0  2  2  1  2 1
  0  2  2 17  2 1
  0  3  0  2  3 1
  0  3  0 17  3 1
  0  3  1  2  2 1
  0  3  1 17  2 1
  0  7  0  1  4 1
  0  7  0  1 10 1
  0  7  2  1  2 1
  0  7  2  1  6 1
  0  7  3  1  2 1
  0  7  3  1  3 1
  0  8  0  2  3 1
  0  8  1  2  2 1
  0  8  2  2  4 1
  0  9  1  3  2 1
  0  9  1 11  2 1
  0 10  0  4  3 1
  0 10  0  4  4 1
  0 10  0  9  4 1
  0 10  0 10  3 1
  1  0  0  0  6 1
  1  0  0  0 21 1
  1  0  0 16  6 1
  1  0  3  0 18 1
  1  0  4 16  2 1
  1  0  5  0  1 1
  1  0  5 15  1 1
  1  0  9  0  6 1
  1  0 10  0  1 1
  1  0 10  0  3 1
  1  0 10 10  1 1
  1  1  0  0  5 1
  1  1  0  0 21 1
  1  1  1  0 20 1
  1  1  4  0  1 1
  1  1  4 16  1 1
  1  1  9 11  1 1
  1  2  0  0 20 1
  1  3  2  2  1 1
  1  3  2 16  1 1
  1  5  0  0  5 1
  1  5  0  0 14 1
  1  5  4  0  1 1
  1  5  4  0  6 1
  1  5  5  0  1 1
  1  5  5  0  3 1
  1  7  2  2  1 1
  1  8  2  3  1 1
  1  8  2 11  1 1
  1 10  0  5  3 1
  1 10  0  5  4 1
  1 10  0  8  4 1
  1 10  0  9  3 1
  2  0  0  0 21 1
  2  0  3  0 18 1
  2  0  6  0  0 1
  2  0  6 14  0 1
  2  0  9 11  0 1
  2  0 10  0  0 1
  2  0 10  0  4 1
  2  0 10  9  0 1
  2  0 10 10  1 1
  2  1  5  0  0 1
  2  1  5 15  0 1
  2  1  8 12  0 1
  2  2  4  1  0 1
  2  2  4 15  0 1
  2  2  8 11  0 1
  2  3  0  0 18 1
  2  4  0  0 16 1
  2  4  5  0  0 1
  2  4  6  0  0 1
  2  4  6  0  4 1
  2  5  4  1  0 1
  2  6  4  2  0 1
  2  6  4 11  0 1
  2  8  2  4  1 1
  2  8  2 10  1 1
  2  9  0  5  6 1
  2  9  0  6  6 1
  2  9  1  5  2 1
  2  9  1  9  2 1
  3  0  6 14  0 1
  3  0  9 11  0 1
  3  0 10  0  0 1
  3  3  0  0 17 1
  3  3  1  0 16 1
  3  3  7  0  0 1
  3  8  0  5  7 1
  3  8  1  5  6 1
  4  0 10  9  0 1
  4  1  0  0  5 1
  4  2  0  0  5 1
  4  6  4  4  0 1
  4  6  4  9  0 1
  4  7  3  5  4 1
  5  0  0  0  6 1
  5  0  0  0 18 1
  5  1  0  0 17 1
  5  1  1  0  4 1
  5  1  5  0  0 1
  5  2  0  1  4 1
  5  2  4  1  0 1
  5  3  0  2  3 1
  5  3  2  2  1 1
  6  0  0  0  7 1
  6  0  0  0 16 1
  6  0  1  0  5 1
  6  0  1  0 16 1
  6  0  6  0  0 1
  6  0  7  0  0 1
  6  0  7  0 10 1
  6  0 10  0  3 1
  6  0 10  0  4 1
  6  0 10  1  0 1
  6  1  9  1  0 1
  6  5  5  5  0 1
  6  5  5  7  0 1
  7  0  0  1  6 1
  7  0  0  1 15 1
  7  0  9  1  0 1
  7  0  9  1  6 1
  7  0 10  1  1 1
  7  0 10  1  4 1
  7  0 10  2  4 1
  7  1  9  2  4 1
  7  3  2  4  1 1
  7  3  2 10  1 1
  8  0  0  2  6 1
  8  0  0  2 13 1
  8  0  0  9  6 1
  8  0 10  2  0 1
  8  0 10  2  3 1
  8  2  4  4  0 1
  8  2  4  9  0 1
  8  3  0  5  3 1
  8  3  0  9  3 1
  8  3  1  5  2 1
  8  3  1  9  2 1
  8  3  7  5  0 1
  9  0 10  3  0 1
  9  0 10  3  1 1
  9  0 10  4  0 1
  9  1  0  4  5 1
  9  1  0  4  9 1
  9  1  0  8  5 1
  9  1  9  4  0 1
  9  2  0  5  4 1
  9  2  0  5  7 1
  9  2  0  8  4 1
 10  0  9  4  0 1
 10  1  1  5  4 1
 10  1  1  5  6 1
 10  1  1  7  4 1
 10  1  5  5  0 1
 10  1  5  7  0 1
 11  0  3  5  3 1
 11  0  3  5  4 1
 11  0  3  6  3 1
 11  0  6  5  0 1
 11  0  6  6  0 1
 11  0  7  5  0 1

32 support hyperplanes:
 -2 -1  0  1 -1 28
 -1 -2 -2  0 -1 31
 -1 -2 -1  0 -1 26
 -1 -1 -1 -1 -1 23
 -1 -1 -1  0  0 19
 -1 -1 -1  2  1 14
 -1 -1 -1  3  1 13
 -1 -1  0  0  0 11
 -1 -1  0  1  0  6
 -1 -1  1  0  2  6
 -1  0  1  0  0  9
 -1  0  2  2  1 -1
 -1  1  1  0  0  8
  0 -2 -2  0 -1 24
  0 -1 -2 -1  1 29
  0 -1 -1  0  0 10
  0  0 -1 -1  0 20
  0  0 -1  0 -1 21
  0  0  0  0  1  0
  0  0  0  1  0  0
  0  0  1  0  0  0
  0  0  1  0  1 -3
  0  0  1  0  2 -4
  0  0  1  1  1 -5
  0  1  0  0  0  0
  0  1  1 -1  0 16
  0  1  1  0  1 -6
  1 -3 -3  1 -1 32
  1  0  0  0  0  0
  1  0  0  0  1 -2
  1  0  0  1  0 -1
  1  1  0 -1  1 13