The Lattice A14
An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, RWTH Aachen University
(nebe@math.rwth-aachen.de)
and
Neil J. A. Sloane
(njasloane@gmail.com)
Last modified Fri Jul 18 13:09:16 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
A14
-
DIMENSION
14
-
DET
15
-
DIVISORS
1 1 1 1 1 1 1 1 1 1 1 1 1 15
-
MINIMAL_NORM
2
-
KISSING_NUMBER
210
-
GROUP_ORDER
2615348736000
-
GROUP_NAME
C2 x S15 = C2 x W(A14)
-
GROUP_GENERATORS
2
14
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 -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 -1 0 0 1
0 0 0 0 0 0 0 0 0 -1 0 0 0 1
0 0 0 0 0 0 0 0 -1 0 0 0 0 1
0 0 0 0 0 0 0 -1 0 0 0 0 0 1
0 0 0 0 0 0 -1 0 0 0 0 0 0 1
0 0 0 0 0 -1 0 0 0 0 0 0 0 1
0 0 0 0 -1 0 0 0 0 0 0 0 0 1
0 0 0 -1 0 0 0 0 0 0 0 0 0 1
0 0 -1 0 0 0 0 0 0 0 0 0 0 1
0 -1 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 1
14
-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 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 -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 -1 0 0 1 0
0 0 0 0 0 0 0 0 -1 0 0 0 1 0
0 0 0 0 0 0 0 -1 0 0 0 0 1 0
0 0 0 0 0 0 -1 0 0 0 0 0 1 0
0 0 0 0 0 -1 0 0 0 0 0 0 1 0
0 0 0 0 -1 0 0 0 0 0 0 0 1 0
0 0 0 -1 0 0 0 0 0 0 0 0 1 0
0 0 -1 0 0 0 0 0 0 0 0 0 1 0
0 -1 0 0 0 0 0 0 0 0 0 0 1 0
-
BASIS
14 15
.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 .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 .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
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.000000000000E+00 .000000000000E+00 .000000000000E+00
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.000000000000E+00 .100000000000E+01 -.100000000000E+01
.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 .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
.100000000000E+01 -.100000000000E+01 .000000000000E+00
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.000000000000E+00 .000000000000E+00 .000000000000E+00
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.000000000000E+00 .100000000000E+01 -.100000000000E+01
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.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
.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 .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 .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
.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 .100000000000E+01 -.100000000000E+01
-
GLUE_VECTORS
15
.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
.666666666667E-01 .666666666667E-01 .666666666667E-01
.666666666667E-01 .666666666667E-01 .666666666667E-01
.666666666667E-01 .666666666667E-01 .666666666667E-01
.666666666667E-01 .666666666667E-01 .666666666667E-01
.666666666667E-01 .666666666667E-01 -.933333333333E+00
.133333333333E+00 .133333333333E+00 .133333333333E+00
.133333333333E+00 .133333333333E+00 .133333333333E+00
.133333333333E+00 .133333333333E+00 .133333333333E+00
.133333333333E+00 .133333333333E+00 .133333333333E+00
.133333333333E+00 -.866666666667E+00 -.866666666667E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
-.800000000000E+00 -.800000000000E+00 -.800000000000E+00
.266666666667E+00 .266666666667E+00 .266666666667E+00
.266666666667E+00 .266666666667E+00 .266666666667E+00
.266666666667E+00 .266666666667E+00 .266666666667E+00
.266666666667E+00 .266666666667E+00 -.733333333333E+00
-.733333333333E+00 -.733333333333E+00 -.733333333333E+00
.333333333333E+00 .333333333333E+00 .333333333333E+00
.333333333333E+00 .333333333333E+00 .333333333333E+00
.333333333333E+00 .333333333333E+00 .333333333333E+00
.333333333333E+00 -.666666666667E+00 -.666666666667E+00
-.666666666667E+00 -.666666666667E+00 -.666666666667E+00
.400000000000E+00 .400000000000E+00 .400000000000E+00
.400000000000E+00 .400000000000E+00 .400000000000E+00
.400000000000E+00 .400000000000E+00 .400000000000E+00
-.600000000000E+00 -.600000000000E+00 -.600000000000E+00
-.600000000000E+00 -.600000000000E+00 -.600000000000E+00
.466666666667E+00 .466666666667E+00 .466666666667E+00
.466666666667E+00 .466666666667E+00 .466666666667E+00
.466666666667E+00 .466666666667E+00 -.533333333333E+00
-.533333333333E+00 -.533333333333E+00 -.533333333333E+00
-.533333333333E+00 -.533333333333E+00 -.533333333333E+00
.533333333333E+00 .533333333333E+00 .533333333333E+00
.533333333333E+00 .533333333333E+00 .533333333333E+00
.533333333333E+00 -.466666666667E+00 -.466666666667E+00
-.466666666667E+00 -.466666666667E+00 -.466666666667E+00
-.466666666667E+00 -.466666666667E+00 -.466666666667E+00
.600000000000E+00 .600000000000E+00 .600000000000E+00
.600000000000E+00 .600000000000E+00 .600000000000E+00
-.400000000000E+00 -.400000000000E+00 -.400000000000E+00
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-.333333333333E+00 -.333333333333E+00 -.333333333333E+00
-.333333333333E+00 -.333333333333E+00 -.333333333333E+00
-.333333333333E+00 -.333333333333E+00 -.333333333333E+00
.733333333333E+00 .733333333333E+00 .733333333333E+00
.733333333333E+00 -.266666666667E+00 -.266666666667E+00
-.266666666667E+00 -.266666666667E+00 -.266666666667E+00
-.266666666667E+00 -.266666666667E+00 -.266666666667E+00
-.266666666667E+00 -.266666666667E+00 -.266666666667E+00
.800000000000E+00 .800000000000E+00 .800000000000E+00
-.200000000000E+00 -.200000000000E+00 -.200000000000E+00
-.200000000000E+00 -.200000000000E+00 -.200000000000E+00
-.200000000000E+00 -.200000000000E+00 -.200000000000E+00
-.200000000000E+00 -.200000000000E+00 -.200000000000E+00
.866666666667E+00 .866666666667E+00 -.133333333333E+00
-.133333333333E+00 -.133333333333E+00 -.133333333333E+00
-.133333333333E+00 -.133333333333E+00 -.133333333333E+00
-.133333333333E+00 -.133333333333E+00 -.133333333333E+00
-.133333333333E+00 -.133333333333E+00 -.133333333333E+00
.933333333333E+00 -.666666666667E-01 -.666666666667E-01
-.666666666667E-01 -.666666666667E-01 -.666666666667E-01
-.666666666667E-01 -.666666666667E-01 -.666666666667E-01
-.666666666667E-01 -.666666666667E-01 -.666666666667E-01
-.666666666667E-01 -.666666666667E-01 -.666666666667E-01
-
TRIANGULAR_BASIS
14 14
.141421356237E+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
-.707106781187E+00 .122474487139E+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 -.816496580928E+00 .115470053838E+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 -.866025403784E+00
.111803398875E+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
-.894427191000E+00 .109544511501E+01 .000000000000E+00
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.000000000000E+00 -.912870929175E+00 .108012344973E+01
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.000000000000E+00 -.942809041582E+00 .105409255339E+01
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.000000000000E+00 .000000000000E+00
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.000000000000E+00 .000000000000E+00 -.948683298051E+00
.104880884817E+01 .000000000000E+00 .000000000000E+00
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.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 -.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 -.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
-.963624111659E+00 .103509833901E+01
-
GRAM
14 14
2 -1 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 -1 2 -1 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 -1 2 -1 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 -1 2 -1 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 -1 2 -1 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 -1 2 -1 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 -1 2 -1
0 0 0 0 0 0 0 0 0 0 0 0 -1 2
-
PROPERTIES
INTEGRAL =1
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe