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

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40 extreme rays
3753 support hyperplanes

embedding dimension = 17
rank = 17 (maximal)

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

40 extreme rays:
 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 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 0 0 0 1 1 1 1
 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 0 1 0 1 1 1
 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1
 0 0 0 0 0 0 0 0 0 0 0 0 1 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 0 0 1 1 0 0 1 1
 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1
 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 0 1 1 1 0 0 0 1
 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 0 1 1 1 0 0 0 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 0 1 1 1 0 0 0 0 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 0 1 1 1 0 0 0 0 0 0 1
 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1
 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1
 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1
 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1
 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1
 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1
 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1
 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1
 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1
 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1
 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1
 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1
 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1
 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1

3753 support hyperplanes:
 0 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 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 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 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 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 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 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 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   0
 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1  -1
 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1 0  -1
 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0  -1
 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 1  -1
 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 1  -1
 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 0  -1
 0 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1  -1
 0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 1  -1
 0 0 1 1 0 0 1 0 1 0 0 1 0 1 0 1  -1
 0 0 1 1 0 0 1 0 1 0 0 1 0 1 1 0  -1
 0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 1  -1
 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 0  -1
 0 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0  -1
 0 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1  -1
 0 0 1 1 0 0 1 0 1 0 1 0 1 0 0 1  -1
 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0  -1
 0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 0  -1
 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 1  -1
 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 1  -1
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 0 0 1 1 0 1 0 0 1 1 0 0 1 0 0 1  -1
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 0 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0  -1
 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1  -1
 0 0 1 1 0 1 0 0 1 1 0 1 0 1 0 1  -1
 0 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0  -1
 0 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1  -1
 0 0 1 1 0 1 0 1 0 1 0 0 1 0 0 1  -1
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 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0  -1
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 0 0 2 2 0 0 2 0 2 0 1 1 1 0 1 1  -2
 0 0 2 2 0 0 2 0 2 0 1 1 1 1 1 0  -2
 0 0 2 2 0 0 2 0 2 0 2 0 1 1 0 1  -2
 0 0 2 2 0 0 2 1 0 1 1 0 1 1 0 1  -2
 0 0 2 2 0 0 2 1 0 1 1 1 0 1 1 1  -2
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 0 0 2 2 0 0 2 2 0 0 2 1 0 1 1 1  -2
 0 0 2 2 0 0 2 2 0 0 2 1 1 0 1 1  -2
 0 0 2 2 0 0 2 2 0 0 2 1 1 1 1 0  -2
 0 0 2 2 0 1 1 0 1 1 0 1 1 0 1 1  -2
 0 0 2 2 0 1 1 0 1 1 0 1 1 1 0 1  -2
 0 0 2 2 0 1 1 0 1 1 0 1 1 1 1 0  -2
 0 0 2 2 0 1 1 0 1 1 0 1 2 0 0 2  -2
 0 0 2 2 0 1 1 0 1 1 0 1 2 0 2 0  -2
 0 0 2 2 0 1 1 0 1 1 0 1 2 2 0 0  -2
 0 0 2 2 0 1 1 0 1 1 0 2 0 0 2 2  -2
 0 0 2 2 0 1 1 0 1 1 0 2 0 1 1 1  -2
 0 0 2 2 0 1 1 0 1 1 0 2 0 2 0 2  -2
 0 0 2 2 0 1 1 0 1 1 0 2 0 2 2 0  -2
 0 0 2 2 0 1 1 0 1 1 1 0 1 1 0 1  -2
 0 0 2 2 0 1 1 0 1 1 1 0 2 0 0 2  -2
 0 0 2 2 0 1 1 0 1 1 1 0 2 0 2 0  -2
 0 0 2 2 0 1 1 0 1 1 1 0 2 2 0 0  -2
 0 0 2 2 0 1 1 0 1 1 1 1 0 1 1 1  -2
 0 0 2 2 0 1 1 0 1 1 2 0 0 2 0 2  -2
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 0 0 2 2 0 1 1 1 0 1 1 0 2 0 0 2  -2
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 0 0 2 2 0 1 1 1 0 1 1 1 0 2 0 2  -2
 0 0 2 2 0 1 1 1 0 1 1 1 1 0 1 1  -2
 0 0 2 2 0 1 1 1 0 1 1 1 1 1 1 0  -2
 0 0 2 2 0 1 1 1 0 1 1 2 0 0 2 2  -2
 0 0 2 2 0 1 1 1 0 1 1 2 0 2 2 0  -2
 0 0 2 2 0 1 1 1 0 1 2 0 0 2 0 2  -2
 0 0 2 2 0 1 1 1 1 0 1 1 0 1 1 1  -2
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 0 0 2 2 0 1 1 1 1 0 1 1 1 1 0 1  -2
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 0 0 2 2 0 1 1 1 1 0 1 1 2 2 0 0  -2
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 0 0 2 2 0 1 1 1 1 0 1 2 0 2 2 0  -2
 0 0 2 2 0 1 1 1 1 0 2 0 0 2 0 2  -2
 0 0 2 2 0 1 1 1 1 0 2 0 1 1 0 1  -2
 0 0 2 2 0 1 1 1 1 0 2 0 2 0 0 2  -2
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 0 0 2 2 0 1 1 1 1 0 2 0 2 2 0 0  -2
 0 0 2 2 0 2 0 0 2 2 0 1 1 0 1 1  -2
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 0 0 2 2 0 2 0 0 2 2 0 1 1 1 1 0  -2
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 0 0 2 2 0 2 0 0 2 2 1 0 1 1 0 1  -2
 0 0 2 2 0 2 0 0 2 2 1 1 0 1 1 1  -2
 0 0 2 2 0 2 0 1 1 1 1 0 1 1 0 1  -2
 0 0 2 2 0 2 0 1 1 1 1 0 2 0 0 2  -2
 0 0 2 2 0 2 0 1 1 1 1 0 2 0 2 0  -2
 0 0 2 2 0 2 0 1 1 1 1 0 2 2 0 0  -2
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 0 0 2 2 1 0 1 1 0 1 2 0 0 2 0 2  -2
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 0 0 2 2 1 1 0 1 1 1 1 1 0 2 0 2  -2
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 0 0 2 2 1 1 0 1 1 1 1 2 0 0 2 2  -2
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 0 0 3 3 0 0 3 0 0 3 0 2 1 1 1 1  -3
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 0 0 3 3 0 0 3 0 2 1 0 2 1 1 1 1  -3
 0 0 3 3 0 0 3 0 2 1 1 1 1 1 1 1  -3
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 0 0 3 3 0 0 3 0 3 0 2 1 1 1 1 1  -3
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 0 0 3 3 0 2 1 1 1 1 1 1 2 0 2 1  -3
 0 0 3 3 0 2 1 1 1 1 1 1 2 1 2 0  -3
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 0 0 3 3 0 2 1 1 1 1 1 1 3 0 0 3  -3
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 0 0 3 3 0 2 1 1 1 1 1 3 0 0 3 3  -3
 0 0 3 3 0 2 1 1 1 1 1 3 0 3 3 0  -3
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 0 0 3 3 0 2 1 1 1 1 2 0 3 0 0 3  -3
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 0 0 3 3 1 1 1 1 1 1 1 2 0 2 2 1  -3
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 0 1 1 0 1 0 0 1 0 1 0 1 0 1 1 0  -1
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 2 0 2 1 0 2 1 1 1 1 1 2 0 1 2 2  -3
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 2 0 2 1 0 2 1 1 1 1 3 0 0 3 0 3  -3
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 2 0 2 1 1 1 1 1 1 1 1 1 1 1 1 1  -3
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 2 0 2 1 1 1 1 1 1 1 1 1 2 0 2 1  -3
 2 0 2 1 1 1 1 1 1 1 1 1 2 1 2 0  -3
 2 0 2 1 1 1 1 1 1 1 1 1 2 2 1 0  -3
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 2 0 2 1 1 1 1 1 1 1 1 1 3 0 3 0  -3
 2 0 2 1 1 1 1 1 1 1 1 1 3 3 0 0  -3
 2 0 2 1 1 1 1 1 1 1 1 2 0 1 2 2  -3
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 2 0 2 1 1 1 1 1 1 1 1 2 0 3 0 3  -3
 2 0 2 1 1 1 1 1 1 1 1 3 0 0 3 3  -3
 2 0 2 1 1 1 1 1 1 1 1 3 0 3 3 0  -3
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 2 0 2 1 1 1 1 1 1 1 2 0 3 3 0 0  -3
 2 0 2 1 1 1 1 1 1 1 3 0 0 3 0 3  -3
 2 0 2 1 2 0 1 2 0 2 1 1 1 1 1 1  -3
 2 0 2 2 0 2 2 0 2 2 1 1 2 1 2 1  -4
 2 0 2 2 0 2 2 1 1 2 1 1 2 1 2 1  -4
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 2 0 2 2 1 1 2 1 1 2 1 1 2 1 2 1  -4
 2 0 2 2 1 1 2 1 2 1 1 2 1 1 2 2  -4
 2 0 2 2 1 1 2 1 2 1 1 2 1 2 2 1  -4
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 2 0 2 2 1 1 2 1 2 1 1 2 2 2 0 2  -4
 2 0 2 2 1 1 2 1 2 1 1 2 2 2 2 0  -4
 2 0 2 2 1 1 2 1 2 1 1 2 4 0 0 4  -4
 2 0 2 2 1 1 2 1 2 1 1 2 4 0 4 0  -4
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 2 2 2 2 3 3 0 3 3 3 3 3 0 3 3 3  -6
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 3 3 0 0 3 1 1 1 1 1 1 2 0 1 2 2  -3
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