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

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16 extreme rays
24 support hyperplanes

embedding dimension = 7
rank = 7 (maximal)
external index = 1

size of triangulation   = 69
resulting sum of |det|s = 72

grading:
1 1 1 1 1 1 -2 

degrees of extreme rays:
1: 16  

multiplicity = 72

Hilbert series:
1 9 31 25 6 
denominator with 7 factors:
1: 7  

degree of Hilbert Series as rational function = -3

Hilbert polynomial:
60 194 284 245 130 41 6 
with common denominator = 60

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

16 extreme rays:
 0 0 0 0 0 1 0
 0 0 0 0 1 0 0
 0 0 0 1 0 0 0
 0 0 1 0 0 0 0
 0 0 1 1 0 1 1
 0 0 1 1 1 0 1
 0 1 0 0 0 0 0
 0 1 0 0 1 1 1
 0 1 0 1 1 0 1
 0 1 1 0 0 1 1
 1 0 0 0 0 0 0
 1 0 0 0 1 1 1
 1 0 0 1 0 1 1
 1 0 1 0 1 0 1
 1 1 0 1 0 0 1
 1 1 1 0 0 0 1

24 support hyperplanes:
 0 0 0 0 0 0  1
 0 0 0 0 0 1  0
 0 0 0 0 1 0  0
 0 0 0 1 0 0  0
 0 0 1 0 0 0  0
 0 0 1 1 0 1 -1
 0 0 1 1 1 0 -1
 0 1 0 0 0 0  0
 0 1 0 0 1 1 -1
 0 1 0 1 1 0 -1
 0 1 1 0 0 1 -1
 0 1 1 1 1 1 -2
 1 0 0 0 0 0  0
 1 0 0 0 1 1 -1
 1 0 0 1 0 1 -1
 1 0 1 0 1 0 -1
 1 0 1 1 1 1 -2
 1 1 0 1 0 0 -1
 1 1 0 1 1 1 -2
 1 1 1 0 0 0 -1
 1 1 1 0 1 1 -2
 1 1 1 1 0 1 -2
 1 1 1 1 1 0 -2
 1 1 1 1 1 1 -3