The Lattice N(4A6)
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 13:20:52 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(4A6)
-
DIMENSION
24
-
DETERMINANT
1
-
MINIMAL_NORM
2
-
KISSING_NUMBER
168
-
DENSITY
.596E-07
-
HERMITE_NUMBER
2
-
GROUP_ORDER
2^19 * 3^9 * 5^4 * 7^4
-
GRAM
24 0
2
1 2
0 1 2
0 1 1 2
0 -1 -1 -1 2
0 0 0 0 0 2
0 0 0 0 0 0 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 -1 2
0 0 0 0 0 0 0 0 -1 1 2
0 0 0 0 0 0 0 0 -1 1 1 2
0 0 0 0 0 0 0 0 0 1 0 0 2
1 1 0 0 -1 -1 0 1 0 0 1 1 -1 4
1 1 0 0 -1 0 -1 -1 0 -1 -1 0 -1 1 4
1 1 0 1 -1 1 1 0 -1 1 1 1 0 1 0 4
1 1 0 1 -1 0 0 0 1 -1 -1 -1 -1 1 2 1 4
1 1 0 0 -1 0 0 0 0 1 1 0 1 1 0 1 0 4
0 1 1 1 0 0 0 0 -1 0 1 1 -1 1 0 1 0 -1 4
1 1 1 0 -1 0 0 0 -1 1 1 1 1 1 0 1 -1 2 0 4
1 1 1 0 -1 0 0 0 -1 1 1 1 1 1 0 1 -1 2 0 3 4
1 1 1 0 -1 0 0 0 -1 0 1 1 -1 2 1 1 0 1 1 2 2 4
0 1 1 1 -1 -1 -1 0 -1 0 1 1 -1 2 1 0 0 0 2 1 1 2 4
0 1 1 1 -1 -1 -1 0 -1 0 1 1 -1 2 1 0 0 0 2 1 1 2 3 4
-
BASIS
24 28
.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
.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 .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
.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 .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 .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 -.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 .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 .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 .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 .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 .100000000000E+01
-.100000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.714285714286E+00 -.285714285714E+00 -.285714285714E+00
-.285714285714E+00 -.285714285714E+00 .714285714286E+00
-.285714285714E+00 -.142857142857E+00 .857142857143E+00
-.142857142857E+00 -.142857142857E+00 -.142857142857E+00
-.142857142857E+00 -.142857142857E+00 .571428571429E+00
-.428571428571E+00 .571428571429E+00 -.428571428571E+00
.571428571429E+00 -.428571428571E+00 -.428571428571E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.714285714286E+00 -.285714285714E+00 -.285714285714E+00
-.285714285714E+00 -.285714285714E+00 .714285714286E+00
-.285714285714E+00 -.142857142857E+00 -.142857142857E+00
-.142857142857E+00 .857142857143E+00 -.142857142857E+00
-.142857142857E+00 -.142857142857E+00 -.428571428571E+00
.571428571429E+00 -.428571428571E+00 -.428571428571E+00
.571428571429E+00 .571428571429E+00 -.428571428571E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.571428571429E+00 -.428571428571E+00 -.428571428571E+00
.571428571429E+00 -.428571428571E+00 .571428571429E+00
-.428571428571E+00 .285714285714E+00 -.714285714286E+00
.285714285714E+00 -.714285714286E+00 .285714285714E+00
.285714285714E+00 .285714285714E+00 -.142857142857E+00
-.142857142857E+00 .857142857143E+00 -.142857142857E+00
-.142857142857E+00 -.142857142857E+00 -.142857142857E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.571428571429E+00 -.428571428571E+00 -.428571428571E+00
.571428571429E+00 -.428571428571E+00 .571428571429E+00
-.428571428571E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .285714285714E+00
.285714285714E+00 -.714285714286E+00 -.714285714286E+00
.285714285714E+00 .285714285714E+00 .285714285714E+00
.857142857143E+00 -.142857142857E+00 -.142857142857E+00
-.142857142857E+00 -.142857142857E+00 -.142857142857E+00
-.142857142857E+00
.571428571429E+00 -.428571428571E+00 -.428571428571E+00
-.428571428571E+00 -.428571428571E+00 .571428571429E+00
.571428571429E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .285714285714E+00
.285714285714E+00 .285714285714E+00 .285714285714E+00
-.714285714286E+00 -.714285714286E+00 .285714285714E+00
-.142857142857E+00 -.142857142857E+00 .857142857143E+00
-.142857142857E+00 -.142857142857E+00 -.142857142857E+00
-.142857142857E+00
.428571428571E+00 .428571428571E+00 .428571428571E+00
.428571428571E+00 -.571428571429E+00 -.571428571429E+00
-.571428571429E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 -.285714285714E+00
-.285714285714E+00 .714285714286E+00 -.285714285714E+00
.714285714286E+00 -.285714285714E+00 -.285714285714E+00
.142857142857E+00 -.857142857143E+00 .142857142857E+00
.142857142857E+00 .142857142857E+00 .142857142857E+00
.142857142857E+00
.428571428571E+00 -.571428571429E+00 .428571428571E+00
-.571428571429E+00 -.571428571429E+00 .428571428571E+00
.428571428571E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 -.285714285714E+00
-.285714285714E+00 .714285714286E+00 .714285714286E+00
-.285714285714E+00 -.285714285714E+00 -.285714285714E+00
.142857142857E+00 .142857142857E+00 .142857142857E+00
.142857142857E+00 .142857142857E+00 .142857142857E+00
-.857142857143E+00
.428571428571E+00 -.571428571429E+00 .428571428571E+00
-.571428571429E+00 -.571428571429E+00 .428571428571E+00
.428571428571E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 -.285714285714E+00
-.285714285714E+00 .714285714286E+00 .714285714286E+00
-.285714285714E+00 -.285714285714E+00 -.285714285714E+00
.142857142857E+00 .142857142857E+00 .142857142857E+00
-.857142857143E+00 .142857142857E+00 .142857142857E+00
.142857142857E+00
.428571428571E+00 -.571428571429E+00 .428571428571E+00
-.571428571429E+00 -.571428571429E+00 .428571428571E+00
.428571428571E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 -.285714285714E+00
-.285714285714E+00 .714285714286E+00 -.285714285714E+00
.714285714286E+00 -.285714285714E+00 -.285714285714E+00
.142857142857E+00 .142857142857E+00 .142857142857E+00
.142857142857E+00 .142857142857E+00 -.857142857143E+00
.142857142857E+00
.142857142857E+00 .142857142857E+00 .142857142857E+00
.142857142857E+00 -.857142857143E+00 .142857142857E+00
.142857142857E+00 -.428571428571E+00 .571428571429E+00
-.428571428571E+00 .571428571429E+00 .571428571429E+00
-.428571428571E+00 -.428571428571E+00 -.285714285714E+00
-.285714285714E+00 .714285714286E+00 -.285714285714E+00
.714285714286E+00 -.285714285714E+00 -.285714285714E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.142857142857E+00 .142857142857E+00 .142857142857E+00
.142857142857E+00 -.857142857143E+00 .142857142857E+00
.142857142857E+00 -.428571428571E+00 .571428571429E+00
-.428571428571E+00 .571428571429E+00 -.428571428571E+00
.571428571429E+00 -.428571428571E+00 -.285714285714E+00
-.285714285714E+00 .714285714286E+00 -.285714285714E+00
.714285714286E+00 -.285714285714E+00 -.285714285714E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
-
ROOT_SYSTEM
4A6
-
NOTES
One of the 24 even unimodular lattices in dimension 24 (the Niemeier lattices)
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe