rational-E.ref

3 extreme rays
3 support hyperplanes

embedding dimension = 3
rank = 3 (maximal)
external index = 1
internal index = 15

size of triangulation   = 1
resulting sum of |det|s = 15

grading:
0 0 1 

degrees of extreme rays:
2: 1  3: 1  4: 1  

multiplicity = 5/8

Weighted Ehrhart series:
-1 -1 -243 -28 -707 -932 -7295 -202 -7963 -16821 -46324 -7083 -47260 -75946 -204427 -40344 -118130 -311050 -612483 3521 -395278 -843516 -1110154 -121555 -926766 -1273327 -2080542 -362431 -1040786 -2200393 -3095094 134801 -1725794 -2980655 -2822488 -142029 -2217716 -2306933 -2898966 -392963 -1413040 -2114089 -2454022 205987 -1246376 -1579905 -1184228 29535 -885785 -618044 -639119 -52785 -308947 -272663 -277707 35989 -124619 -93336 -55364 6892 -37032 -11189 -9663 -89 -4150 -713 -759 64 -130 -7 -2 
Common denominator of coefficients: 1
Series denominator with 8 factors:
1: 1  2: 1  12: 6  
shift = 2


degree of weighted Ehrhart series as rational function = -3

Weighted Ehrhart series with cyclotomic denominator:
-1 -7 -270 -1557 -6112 -18086 -49651 -122957 -273914 -532596 -920135 -1438520 -2090015 -2834874 -3584981 -4189870 -4535739 -4576125 -4346826 -3880606 -3235830 -2484701 -1753577 -1137214 -684948 -378881 -190855 -83993 -32747 -11191 -3623 -963 -214 -19 -2 
Common denominator of coefficients: 1
Series cyclotomic denominator:
1: 8  2: 7  3: 6  4: 6  

Weighted Ehrhart quasi-polynomial of period 12:
  0:          0  101772288 42329952 -11592504 -7856100 -1154160 -142436 -22605
  1:   71639953  -80870403 -2027991  12275473  -294525  -603393  -96509 -22605
  2:  -93231488   51555744 29564304  -9768136 -2452380  -450660 -142436 -22605
  3:  -68324067 -111211623 -3153087  19918521  2171295  -802053  -96509 -22605
  4:  -17841152   93106176 49211232 -10295096 -8178660 -1261680 -142436 -22605
  5:   72672145  -60205059 -1834455  12067601   -79485  -710913  -96509 -22605
  6:  -76422528   39556512 22489488 -10857672 -2344860  -235620 -142436 -22605
  7:  -86165219 -119877735  3728193  21215929  1848735  -909573  -96509 -22605
  8:  -16808960  113771520 49404768 -10502968 -7963620 -1369200 -142436 -22605
  9:   89481105  -72204291 -8909271  10978065    28035  -495873  -96509 -22605
 10:  -94263680   30890400 29370768  -9560264 -2667420  -343140 -142436 -22605
 11:  -85133027  -99212391  3921729  21008057  2063775 -1017093  -96509 -22605
with common denominator: 15676416


Degree of (quasi)polynomial: 7

Expected degree: 7

Virtual multiplicity: -37675/5184

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3 extreme rays:
  1  1 2
 -1 -1 3
  1 -2 4

3 support hyperplanes:
 -8  2 3
  1 -1 0
  2  7 3