The Lattice N(6A4)
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 13:20:57 CEST 2014
INDEX FILE 
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DETERMINANT
MINIMAL_NORM
KISSING_NUMBER
DENSITY
HERMITE_NUMBER
GROUP_ORDER
GRAM
BASIS
ROOT_SYSTEM
NOTES
LAST_LINE

NAME
N(6A4)

DIMENSION
24

DETERMINANT
1

MINIMAL_NORM
2

KISSING_NUMBER
120

DENSITY
.596E07

HERMITE_NUMBER
2

GROUP_ORDER
2^22 * 3^7 * 5^7

GRAM
24 0
2
1 2
1 1 2
0 0 0 2
0 0 0 0 2
0 0 0 0 0 2
0 0 0 0 0 1 2
0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 1 2
0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 1 0 1 2
1 0 1 1 1 0 0 1 1 1 1 4
1 0 1 0 0 0 1 1 1 1 0 1 4
1 0 1 0 0 0 1 1 1 1 0 1 3 4
1 1 1 1 1 1 1 0 0 1 1 0 0 0 4
1 1 1 1 0 1 1 1 1 0 0 2 0 0 1 4
1 1 1 1 0 1 1 1 1 0 0 2 0 0 1 3 4
1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 4
1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 1 1 1 4
1 1 1 0 1 1 1 1 1 1 0 0 2 2 0 1 1 0 0 4
1 1 1 0 1 1 1 1 1 1 0 1 2 2 1 1 1 0 0 2 4
1 1 1 0 1 1 1 1 0 1 1 2 1 1 1 2 2 1 1 1 2 4
0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 2 2 0 0 1 0 1 4
0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 2 2 0 0 1 0 1 3 4

BASIS
24 30
.100000000000E+01 .000000000000E+00 .000000000000E+00
.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 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .100000000000E+01 .000000000000E+00
.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 .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 .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 .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 .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 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .100000000000E+01
.000000000000E+00 .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 .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
.000000000000E+00 .000000000000E+00 .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
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .100000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.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 .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 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.100000000000E+01 .000000000000E+00 .100000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.400000000000E+00 .600000000000E+00 .400000000000E+00
.600000000000E+00 .400000000000E+00 .200000000000E+00
.800000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.800000000000E+00 .200000000000E+00 .200000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .600000000000E+00
.600000000000E+00 .400000000000E+00 .400000000000E+00
.400000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.400000000000E+00 .600000000000E+00 .400000000000E+00
.600000000000E+00 .400000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .800000000000E+00 .600000000000E+00
.400000000000E+00 .600000000000E+00 .400000000000E+00
.400000000000E+00 .800000000000E+00 .200000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.400000000000E+00 .600000000000E+00 .400000000000E+00
.600000000000E+00 .400000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .800000000000E+00 .600000000000E+00
.400000000000E+00 .600000000000E+00 .400000000000E+00
.400000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .200000000000E+00 .800000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.800000000000E+00 .200000000000E+00 .200000000000E+00
.800000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.800000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .200000000000E+00 .800000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.800000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.800000000000E+00 .200000000000E+00 .200000000000E+00
.800000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+00 .200000000000E+00 .800000000000E+00
.200000000000E+00 .200000000000E+00 .800000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .200000000000E+00 .800000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.800000000000E+00 .200000000000E+00 .200000000000E+00
.800000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+00 .200000000000E+00 .800000000000E+00
.200000000000E+00 .200000000000E+00 .800000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .800000000000E+00 .200000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.800000000000E+00 .200000000000E+00 .200000000000E+00
.800000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.600000000000E+00 .400000000000E+00 .600000000000E+00
.400000000000E+00 .400000000000E+00 .600000000000E+00
.600000000000E+00 .400000000000E+00 .400000000000E+00
.400000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.800000000000E+00 .200000000000E+00 .200000000000E+00
.800000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.400000000000E+00 .400000000000E+00 .400000000000E+00
.600000000000E+00 .600000000000E+00 .600000000000E+00
.400000000000E+00 .600000000000E+00 .400000000000E+00
.400000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.800000000000E+00 .200000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .400000000000E+00 .400000000000E+00
.400000000000E+00 .600000000000E+00 .600000000000E+00
.200000000000E+00 .200000000000E+00 .800000000000E+00
.200000000000E+00 .200000000000E+00 .600000000000E+00
.400000000000E+00 .600000000000E+00 .400000000000E+00
.400000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.800000000000E+00 .200000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .400000000000E+00 .600000000000E+00
.600000000000E+00 .400000000000E+00 .400000000000E+00
.200000000000E+00 .200000000000E+00 .800000000000E+00
.200000000000E+00 .200000000000E+00 .600000000000E+00
.400000000000E+00 .600000000000E+00 .400000000000E+00
.400000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.800000000000E+00 .200000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .600000000000E+00 .400000000000E+00
.600000000000E+00 .400000000000E+00 .400000000000E+00
.200000000000E+00 .200000000000E+00 .800000000000E+00
.200000000000E+00 .200000000000E+00 .400000000000E+00
.400000000000E+00 .600000000000E+00 .600000000000E+00
.400000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .400000000000E+00
.600000000000E+00 .400000000000E+00 .600000000000E+00
.400000000000E+00 .200000000000E+00 .200000000000E+00
.800000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .200000000000E+00 .800000000000E+00
.200000000000E+00 .200000000000E+00 .600000000000E+00
.600000000000E+00 .400000000000E+00 .400000000000E+00
.400000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .400000000000E+00
.600000000000E+00 .600000000000E+00 .400000000000E+00
.400000000000E+00 .200000000000E+00 .200000000000E+00
.800000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 .200000000000E+00 .800000000000E+00
.200000000000E+00 .200000000000E+00 .600000000000E+00
.600000000000E+00 .400000000000E+00 .400000000000E+00
.400000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00

ROOT_SYSTEM
6A4

NOTES
One of the 24 even unimodular lattices in dimension 24 (the Niemeier lattices)

LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe