The Lattice A18
An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, RWTH Aachen University
(nebe@math.rwthaachen.de)
and
Neil J. A. Sloane
(njasloane@gmail.com)
Last modified Fri Jul 18 13:09:27 CEST 2014
INDEX FILE 
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
DIVISORS
MINIMAL_NORM
KISSING_NUMBER
GROUP_ORDER
GROUP_NAME
GROUP_GENERATORS
BASIS
GLUE_VECTORS
TRIANGULAR_BASIS
GRAM
PROPERTIES
LAST_LINE

NAME
A18

DIMENSION
18

DET
19

DIVISORS
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 19

MINIMAL_NORM
2

KISSING_NUMBER
342

GROUP_ORDER
243290200817664000

GROUP_NAME
C2 x S19 = C2 x W(A18)

GROUP_GENERATORS
2
18
0 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
0 1 1
0 0 0 0 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 1
0 0 1
0 0 0 0 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 1 0 0
0 0 1
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 1
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 1
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 1
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 1
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 1
0 0 0 0 0 0 1 0 0 0 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 1
0 0 0 0 1 0 0 0 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 1
0 0 1 0 0 0 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 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1
18
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
0 1 1
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 0
1 1 0
0 0 0 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 1 0
0 1 0
0 0 0 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 1 0 0 0
0 1 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 1 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 1 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 1 0
0 0 0 0 0 1 0 0 0 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 1 0
0 0 0 1 0 0 0 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 1 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0

BASIS
18 19
.100000000000E+01 .100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.000000000000E+00 .100000000000E+01 .100000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.000000000000E+00 .000000000000E+00 .100000000000E+01
.100000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.100000000000E+01 .100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .100000000000E+01 .100000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
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.000000000000E+00 .100000000000E+01 .100000000000E+01
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.000000000000E+00 .100000000000E+01 .100000000000E+01
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.000000000000E+00
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.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .100000000000E+01
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.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
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.000000000000E+00
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.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .100000000000E+01 .100000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
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.000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
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.000000000000E+00 .000000000000E+00 .000000000000E+00
.100000000000E+01 .100000000000E+01 .000000000000E+00
.000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
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.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .100000000000E+01 .100000000000E+01
.000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .100000000000E+01
.100000000000E+01

GLUE_VECTORS
19
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
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.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
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.526315789474E01 .526315789474E01 .526315789474E01
.526315789474E01 .526315789474E01 .526315789474E01
.526315789474E01 .526315789474E01 .526315789474E01
.526315789474E01 .526315789474E01 .526315789474E01
.526315789474E01 .526315789474E01 .526315789474E01
.947368421053E+00
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.105263157895E+00 .105263157895E+00 .105263157895E+00
.105263157895E+00 .105263157895E+00 .105263157895E+00
.105263157895E+00 .105263157895E+00 .105263157895E+00
.105263157895E+00 .105263157895E+00 .105263157895E+00
.105263157895E+00 .105263157895E+00 .894736842105E+00
.894736842105E+00
.157894736842E+00 .157894736842E+00 .157894736842E+00
.157894736842E+00 .157894736842E+00 .157894736842E+00
.157894736842E+00 .157894736842E+00 .157894736842E+00
.157894736842E+00 .157894736842E+00 .157894736842E+00
.157894736842E+00 .157894736842E+00 .157894736842E+00
.157894736842E+00 .842105263158E+00 .842105263158E+00
.842105263158E+00
.210526315789E+00 .210526315789E+00 .210526315789E+00
.210526315789E+00 .210526315789E+00 .210526315789E+00
.210526315789E+00 .210526315789E+00 .210526315789E+00
.210526315789E+00 .210526315789E+00 .210526315789E+00
.210526315789E+00 .210526315789E+00 .210526315789E+00
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.789473684211E+00
.263157894737E+00 .263157894737E+00 .263157894737E+00
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.263157894737E+00 .263157894737E+00 .736842105263E+00
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.631578947368E+00 .631578947368E+00 .631578947368E+00
.631578947368E+00 .631578947368E+00 .631578947368E+00
.631578947368E+00
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.421052631579E+00 .421052631579E+00 .421052631579E+00
.421052631579E+00 .421052631579E+00 .578947368421E+00
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.578947368421E+00
.473684210526E+00 .473684210526E+00 .473684210526E+00
.473684210526E+00 .473684210526E+00 .473684210526E+00
.473684210526E+00 .473684210526E+00 .473684210526E+00
.473684210526E+00 .526315789474E+00 .526315789474E+00
.526315789474E+00 .526315789474E+00 .526315789474E+00
.526315789474E+00 .526315789474E+00 .526315789474E+00
.526315789474E+00
.526315789474E+00 .526315789474E+00 .526315789474E+00
.526315789474E+00 .526315789474E+00 .526315789474E+00
.526315789474E+00 .526315789474E+00 .526315789474E+00
.473684210526E+00 .473684210526E+00 .473684210526E+00
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.473684210526E+00
.578947368421E+00 .578947368421E+00 .578947368421E+00
.578947368421E+00 .578947368421E+00 .578947368421E+00
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.421052631579E+00 .421052631579E+00 .421052631579E+00
.421052631579E+00 .421052631579E+00 .421052631579E+00
.421052631579E+00 .421052631579E+00 .421052631579E+00
.421052631579E+00
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.368421052632E+00
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.315789473684E+00 .315789473684E+00 .315789473684E+00
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.315789473684E+00 .315789473684E+00 .315789473684E+00
.315789473684E+00 .315789473684E+00 .315789473684E+00
.315789473684E+00
.736842105263E+00 .736842105263E+00 .736842105263E+00
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.263157894737E+00 .263157894737E+00 .263157894737E+00
.263157894737E+00 .263157894737E+00 .263157894737E+00
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.263157894737E+00
.789473684211E+00 .789473684211E+00 .789473684211E+00
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.210526315789E+00 .210526315789E+00 .210526315789E+00
.210526315789E+00 .210526315789E+00 .210526315789E+00
.210526315789E+00 .210526315789E+00 .210526315789E+00
.210526315789E+00 .210526315789E+00 .210526315789E+00
.210526315789E+00
.842105263158E+00 .842105263158E+00 .842105263158E+00
.157894736842E+00 .157894736842E+00 .157894736842E+00
.157894736842E+00 .157894736842E+00 .157894736842E+00
.157894736842E+00 .157894736842E+00 .157894736842E+00
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.157894736842E+00
.894736842105E+00 .894736842105E+00 .105263157895E+00
.105263157895E+00 .105263157895E+00 .105263157895E+00
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.105263157895E+00 .105263157895E+00 .105263157895E+00
.105263157895E+00 .105263157895E+00 .105263157895E+00
.105263157895E+00 .105263157895E+00 .105263157895E+00
.105263157895E+00
.947368421053E+00 .526315789474E01 .526315789474E01
.526315789474E01 .526315789474E01 .526315789474E01
.526315789474E01 .526315789474E01 .526315789474E01
.526315789474E01 .526315789474E01 .526315789474E01
.526315789474E01 .526315789474E01 .526315789474E01
.526315789474E01 .526315789474E01 .526315789474E01
.526315789474E01

TRIANGULAR_BASIS
18 18
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.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .912870929175E+00 .108012344973E+01
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.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.953462589246E+00 .104446593573E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .957427107756E+00 .104083299973E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .960768922831E+00
.103774904333E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.963624111659E+00 .103509833901E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .966091783079E+00 .103279555899E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .968245836552E+00
.103077640640E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.970142500145E+00 .102899151086E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .971825315808E+00 .102740233383E+01

GRAM
18 18
2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0
1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0
0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0
0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0
0 0
0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0
0 0
0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0
0 0
0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0
0 0
0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0
0 0
0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0
0 0
0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0
0 0
0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0
0 0
0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0
0 0
0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0
0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0
0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1
0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2
1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
2 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2

PROPERTIES
INTEGRAL =1

LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe