The Lattice L6(P^6)
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 13:11:09 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
GRAM
MINIMAL_NORM
KISSING_NUMBER
HERMITIAN_GROUP_ORDER
HERMITIAN_GROUP_GENERATORS
HERMITIAN_STRUCTURE
PROPERTIES
REFERENCES
NOTES
LAST_LINE
-
NAME
L6(P^6)
-
DIMENSION
24
-
DET
1
-
GRAM
24 24
8 0 0 -4 -2 2 0 0 -4 0 -2 2 0 2 0 2 2 0 0 -2 0 2 -2 0
0 8 0 4 -2 -2 -4 -2 0 -4 2 0 -2 0 2 2 0 2 -2 0 -2 0 0 2
0 0 8 4 0 4 -2 2 2 -2 -4 -4 0 -2 0 0 0 2 2 2 2 0 0 0
-4 4 4 8 2 0 -4 -2 2 -4 0 -4 -2 -2 0 0 0 2 0 2 0 -2 0 0
-2 -2 0 2 8 0 0 -4 0 0 2 0 2 -2 -2 -4 -2 -2 2 2 2 -2 0 -2
2 -2 4 0 0 8 0 4 0 0 -2 -2 2 2 -2 0 2 -2 2 -2 2 2 0 0
0 -4 -2 -4 0 0 8 4 -2 2 0 2 2 2 2 0 -2 -2 -2 -2 0 0 2 0
0 -2 2 -2 -4 4 4 8 0 2 -2 0 2 2 2 2 0 0 0 -2 0 2 2 2
-4 0 2 2 0 0 -2 0 8 0 0 -4 2 -2 -2 -4 -2 -2 2 2 2 -2 0 -2
0 -4 -2 -4 0 0 2 2 0 8 0 4 2 2 -2 0 2 -2 2 -2 2 2 0 0
-2 2 -4 0 2 -2 0 -2 0 0 8 4 2 2 2 0 -2 -2 -2 -2 0 0 2 0
2 0 -4 -4 0 -2 2 0 -4 4 4 8 2 2 2 2 0 0 0 -2 0 2 2 2
0 -2 0 -2 2 2 2 2 2 2 2 2 8 0 0 -4 -4 -2 2 0 2 0 2 0
2 0 -2 -2 -2 2 2 2 -2 2 2 2 0 8 0 4 2 -4 -4 -6 0 2 0 0
0 2 0 0 -2 -2 2 2 -2 -2 2 2 0 0 8 4 -2 4 -4 0 -2 0 2 2
2 2 0 0 -4 0 0 2 -4 0 0 2 -4 4 4 8 4 2 -4 -4 -2 2 0 2
2 0 0 0 -2 2 -2 0 -2 2 -2 0 -4 2 -2 4 8 0 0 -4 0 2 -2 0
0 2 2 2 -2 -2 -2 0 -2 -2 -2 0 -2 -4 4 2 0 8 0 4 -2 0 0 2
0 -2 2 0 2 2 -2 0 2 2 -2 0 2 -4 -4 -4 0 0 8 4 2 0 0 0
-2 0 2 2 2 -2 -2 -2 2 -2 -2 -2 0 -6 0 -4 -4 4 4 8 0 -2 0 0
0 -2 2 0 2 2 0 0 2 2 0 0 2 0 -2 -2 0 -2 2 0 4 0 0 -2
2 0 0 -2 -2 2 0 2 -2 2 0 2 0 2 0 2 2 0 0 -2 0 4 0 2
-2 0 0 0 0 0 2 2 0 0 2 2 2 0 2 0 -2 0 0 0 0 0 4 2
0 2 0 0 -2 0 0 2 -2 0 0 2 0 0 2 2 0 2 0 0 -2 2 2 4
-
MINIMAL_NORM
2
-
KISSING_NUMBER
6*24
-
HERMITIAN_GROUP_ORDER
2^21 * 3^3 * 5
-
HERMITIAN_GROUP_GENERATORS
7
24 24
-1 1 1 -2 0 0 0 -2 -1 1 0 -2 0 1 1 0 -1 1 2 -2 0 0 0 0
0 0 -1 0 2 0 -2 2 1 -1 -2 2 -2 1 1 -2 -1 1 0 -2 0 0 0 0
0 1 0 0 0 2 2 -2 1 1 0 0 0 -1 -1 2 -1 1 0 0 0 0 0 0
1 0 -1 1 2 0 0 2 2 -1 -1 2 -1 0 -1 0 0 1 -1 0 0 0 0 0
1 0 1 0 1 -2 0 2 0 -1 1 0 1 0 -1 0 2 -1 -1 2 0 0 0 0
-1 2 1 -2 0 1 2 -2 0 1 1 -2 1 0 -1 2 0 1 1 0 0 0 0 0
-1 0 1 0 -2 0 1 -2 -2 1 1 -2 1 0 1 0 0 -1 1 0 0 0 0 0
-1 1 0 0 -2 2 2 -3 -1 2 1 -2 1 -1 0 2 -1 0 1 0 0 0 0 0
1 -1 -2 2 0 2 0 0 2 0 -1 2 -1 -1 0 0 -1 0 -1 0 0 0 0 0
1 -1 0 2 -2 0 0 0 -1 1 1 0 1 -1 0 0 1 -2 -1 2 0 0 0 0
1 -1 0 0 2 -2 -2 4 1 -2 0 2 -1 1 0 -2 1 0 -1 0 0 0 0 0
0 -1 1 0 0 -2 -2 2 -1 -1 0 1 0 1 1 -2 1 -1 0 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 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 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 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 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 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 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 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 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 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 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 0 0 0 0 0 0 0 1
24 24
0 -1 1 0 0 0 0 0 0 0 1 0 0 0 0 -1 1 0 -1 0 0 -1 -1 2
0 1 1 -2 0 0 0 0 -1 1 1 -2 1 0 -1 1 1 0 -1 2 0 -1 1 0
-2 1 1 -2 0 0 0 0 -1 0 0 0 0 1 1 -1 1 0 1 0 0 -1 -1 0
-1 2 1 -2 0 0 0 0 -1 1 0 -1 1 0 0 1 1 -1 0 2 -1 0 1 -2
0 1 0 1 -1 1 1 -1 0 1 0 0 1 -1 0 1 0 -1 0 1 -1 1 0 -1
-2 0 1 -1 -1 0 0 -1 -1 0 0 0 0 1 1 -1 0 0 1 -1 0 -1 -1 1
1 -2 -2 3 0 0 -1 1 1 -1 -1 2 -1 0 1 -1 -1 0 0 -1 1 0 -1 1
-1 -1 -1 0 0 0 -1 0 0 -1 -1 1 -1 1 1 -1 -1 1 1 -2 1 -1 -1 1
-1 1 0 -1 0 0 0 0 -1 0 -1 0 0 0 0 0 -1 0 1 -1 0 0 0 -1
0 -1 -1 1 0 0 0 0 1 -2 -1 2 0 0 0 0 0 0 0 -1 1 0 -1 1
1 0 -1 1 0 0 0 0 1 0 -1 0 0 0 0 0 -1 1 0 -1 0 1 1 -1
1 -1 -1 1 0 0 0 0 1 -1 0 0 0 0 0 0 0 1 0 -1 1 0 0 1
-1 0 -1 0 0 0 0 0 0 -1 -1 0 0 0 0 0 -1 1 1 -2 1 0 -1 1
1 -2 -1 2 0 0 0 0 2 -1 -1 2 0 0 0 0 0 0 -1 0 0 0 0 1
1 0 -1 0 0 0 0 0 0 1 1 -2 0 0 0 0 0 1 0 0 1 -1 0 1
1 -1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 -1 1 0 -1 0 1
0 0 1 -1 0 0 0 0 0 0 1 0 0 0 0 0 1 -1 -1 1 0 -1 0 1
0 1 0 -1 0 0 0 0 -1 1 1 -2 0 0 0 0 1 0 0 1 0 0 1 -1
-1 1 1 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 -1 -1 0 0 -1
0 1 0 0 0 0 0 0 -1 1 0 -1 0 0 0 0 0 0 1 0 -1 1 1 -2
-1 0 0 0 0 0 0 0 0 -1 -1 1 0 1 1 -1 0 0 1 -1 0 0 -1 0
0 -1 0 0 0 0 0 0 1 -1 0 1 -1 1 0 -1 0 1 0 -1 1 -1 -1 2
0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 1 -1 1 1 -1 1 0 0 0
0 0 0 -1 0 0 0 0 0 0 1 -1 0 0 -1 1 0 1 0 0 1 -1 0 1
24 24
-1 1 0 -1 0 0 0 0 0 0 0 0 0 0 -1 1 -1 1 1 -1 0 0 0 -1
0 -1 -1 1 0 0 0 0 0 0 0 0 0 -1 0 1 -1 0 0 -1 1 0 -1 1
1 0 -1 1 0 0 0 0 0 0 0 0 1 -1 -1 1 0 0 -1 1 0 1 1 -1
1 -1 -1 1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -1 0 1 0 0 1
0 0 1 -1 0 -1 -1 1 -1 0 0 0 0 0 0 -1 1 -1 -1 1 0 -1 0 1
0 1 0 -1 1 -1 0 1 0 -1 0 0 1 0 -1 1 1 0 0 1 0 0 1 -1
-1 1 1 -1 0 0 0 -1 0 0 -1 0 0 1 1 -1 0 0 1 -1 -1 0 0 -1
0 1 0 0 0 0 1 -1 0 0 0 -1 1 0 0 1 0 0 1 0 -1 1 1 -2
1 -1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 -1 -1 2 0 0 0 1
0 1 1 -1 0 0 0 0 -1 1 1 -2 0 0 0 0 0 0 1 0 -1 0 1 -1
-1 0 1 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 -1 -1 1
-1 1 1 -1 0 0 0 0 -1 1 0 -1 0 0 0 0 -1 0 1 -1 -1 0 0 -1
0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 -1 0 1 -2 0 0 -1
-1 1 1 -2 0 0 0 0 -1 0 1 -1 0 0 0 0 0 0 1 -1 1 -2 -1 1
-1 0 0 0 0 0 0 0 0 -1 -1 1 0 0 0 0 -1 0 0 -1 0 1 -1 -1
-1 1 0 -1 0 0 0 0 -1 0 0 -1 0 0 0 0 -1 1 1 -2 1 0 0 -1
-1 1 0 -1 0 0 0 0 -1 0 0 -1 0 0 0 0 0 1 1 -1 1 0 1 -1
0 -1 -1 1 0 0 0 0 1 -1 -1 1 0 0 0 0 -1 1 0 -1 0 2 0 -1
1 0 -1 1 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 1 -1 1 2 -1
1 -1 -1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 1 0 1 0 1
0 1 1 -1 0 0 0 0 -1 1 1 -1 1 -1 -1 1 1 -1 -1 2 -1 0 1 -1
-1 1 0 -1 0 0 0 0 -1 0 0 -1 1 0 0 1 0 0 1 0 0 0 0 -1
0 0 0 1 0 0 0 0 0 0 -1 1 0 0 1 -1 0 -1 0 0 -1 1 0 -1
0 0 -1 1 0 0 0 0 0 0 -1 0 0 0 1 0 -1 0 1 -1 0 1 0 -1
24 24
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 0
0 0 0 0 0 0 0 0 -1 0 1 -1 0 0 0 0 0 0 0 0 1 -1 -1 2
0 0 0 0 0 0 0 0 0 -1 -1 1 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 -1 0 0 -1 0 0 0 0 0 0 0 0 1 -1 0 1
-1 0 1 -2 0 -1 0 0 -1 0 1 -2 0 1 0 0 0 1 1 -1 2 -2 -1 2
1 0 -1 0 1 0 0 0 1 0 -1 0 -1 0 0 0 -1 1 0 -1 1 1 1 0
-1 2 1 -2 -1 1 1 -2 -1 2 1 -2 1 -1 -1 2 0 0 0 1 -1 0 2 -2
1 1 0 0 0 1 1 -1 1 1 0 0 0 -1 -1 1 0 0 -1 1 -1 1 2 -1
1 -1 -1 1 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 1 0 0 1
1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 -1 1 1 -1
0 0 1 -1 0 0 0 0 -1 1 2 -2 0 0 0 0 0 0 0 0 0 -1 0 1
0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 -1 0 0 0
1 -1 0 0 0 0 0 0 1 0 1 0 -1 0 0 0 0 0 0 0 1 -1 0 2
1 1 0 0 0 0 0 0 -1 2 1 -2 0 -1 0 0 0 0 0 0 -1 1 2 -2
-1 1 2 -2 0 0 0 0 -1 0 1 0 0 0 -1 0 0 0 0 0 -1 -1 0 0
0 1 1 0 0 0 0 0 -1 1 0 0 0 0 0 -1 0 0 0 0 -2 1 1 -2
1 0 -1 2 0 0 0 0 0 1 -1 0 0 0 0 0 -1 0 0 0 -1 2 1 -2
-1 0 1 0 0 0 0 0 0 -1 -1 2 0 0 0 0 0 -1 0 0 -1 0 -1 0
1 -2 -1 2 0 0 0 0 2 -1 -1 2 0 0 0 0 0 0 -1 0 1 0 -1 2
-1 -1 0 0 0 0 0 0 1 -2 -1 2 0 0 0 0 0 0 0 -1 1 -1 -2 2
0 0 0 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 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 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 0 0 0 0 0 0 0 1
24 24
0 1 1 -1 0 0 0 0 -1 1 1 -1 2 -1 -1 2 1 -1 -1 2 -1 0 0 -1
-1 1 0 -1 0 0 0 0 -1 0 0 -1 0 1 1 0 0 0 1 0 1 -1 -1 1
0 0 0 1 0 0 0 0 0 0 -1 1 0 -1 1 0 0 -1 0 0 0 1 0 -1
0 0 -1 1 0 0 0 0 0 0 -1 0 -1 0 1 0 -1 0 1 -1 1 0 0 0
0 1 0 -1 -1 1 1 -2 -1 2 1 -3 0 -1 -1 2 -2 1 1 -1 1 -1 1 0
0 0 -1 1 0 0 -1 0 0 0 -2 1 0 -1 1 0 -1 -1 0 -1 0 2 1 -2
1 0 0 1 0 1 0 0 1 1 0 1 0 -1 -1 0 0 0 -2 1 -2 1 2 -2
1 -1 -1 2 1 0 -1 1 2 -1 -2 3 -1 0 1 -2 0 0 -1 -1 -1 2 1 -1
0 -1 -1 1 0 0 0 0 1 -1 -1 1 -1 1 2 -2 0 0 1 -1 1 0 -1 1
1 -1 0 1 0 0 0 0 1 0 0 1 -1 1 0 -2 0 1 0 -1 0 0 0 1
0 0 0 -1 0 0 0 0 0 0 1 -1 -1 1 0 0 -1 1 1 -1 1 -1 0 1
0 0 1 -1 0 0 0 0 0 0 1 0 0 1 -1 0 0 1 0 0 0 -1 0 1
1 0 -1 0 1 1 0 0 2 0 -1 1 -1 0 0 0 -1 1 0 -1 0 0 1 0
1 0 -1 2 -1 1 0 0 0 1 0 1 0 -1 0 0 0 -1 -1 1 -1 1 1 -2
1 0 1 0 1 -1 0 2 1 -1 1 1 0 0 -1 0 1 0 -1 1 -1 0 0 0
1 -1 0 2 0 -1 -1 2 0 -1 0 2 0 0 0 -1 1 -1 -1 1 -1 1 0 -1
0 -1 0 1 0 -2 -2 2 -1 -1 -1 1 0 1 1 -2 1 -1 0 0 0 1 0 -1
0 0 1 -1 2 -2 0 2 1 -2 0 1 0 1 -1 0 1 1 0 0 0 0 -1 1
-1 0 0 -1 0 0 0 -2 0 0 -1 -1 0 1 1 0 -1 1 2 -2 1 0 0 1
-1 1 1 -2 0 0 2 -2 0 0 1 -2 1 0 -1 2 0 1 1 0 1 -1 -1 2
0 0 0 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 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 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 0 0 0 0 0 0 0 1
24 24
0 1 1 -2 1 -1 0 0 0 0 0 -1 0 1 0 0 0 1 1 -1 0 0 0 0
0 1 -1 0 1 1 0 0 1 0 -1 1 -1 0 0 0 -1 1 0 -1 0 0 0 0
0 1 1 0 -1 1 2 -2 0 1 1 -1 1 -1 -1 2 0 0 0 1 0 0 0 0
1 0 -1 2 0 1 1 0 1 0 0 1 0 -1 -1 1 0 0 -1 1 0 0 0 0
1 -1 0 1 1 -1 -1 2 0 -1 0 1 0 0 0 -1 1 -1 -1 1 0 0 0 0
0 1 1 -1 0 0 1 0 0 0 1 -1 1 0 -1 1 1 0 0 1 0 0 0 0
-1 0 1 -1 0 -1 0 0 -1 0 0 -1 0 1 1 -1 0 0 1 -1 0 0 0 0
-1 1 1 -1 -1 0 1 -1 -1 1 1 -2 1 0 0 1 0 0 1 0 0 0 0 0
0 0 -1 1 -1 2 1 -2 1 1 0 0 0 -1 0 1 -1 0 0 0 0 0 0 0
0 -1 0 1 -1 0 -1 0 -1 1 0 0 0 0 1 -1 0 -1 0 0 0 0 0 0
1 -1 -1 1 1 0 -1 2 1 -1 0 2 -1 0 0 -1 0 0 -1 0 0 0 0 0
0 -1 0 0 1 -1 -2 2 0 -1 -1 2 -1 1 1 -2 0 0 0 -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 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 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 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 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 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 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 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 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 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 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 0 0 0 0 0 0 0 1
24 24
-2 1 0 -2 0 0 0 -1 -1 -1 -1 -1 0 1 0 0 -1 1 2 -2 1 0 0 0
1 -2 -2 2 1 0 -1 1 3 -2 -2 3 -1 0 0 0 -1 1 0 -2 0 1 0 0
1 1 -1 0 0 1 1 -1 0 2 1 -3 1 -1 -1 2 -1 1 0 0 0 0 1 0
2 -1 -1 1 1 0 0 1 2 0 1 0 0 -1 -1 1 0 1 -1 0 0 0 0 1
1 0 1 -1 1 -1 0 2 0 0 2 -1 0 0 -1 0 2 0 -1 2 0 -1 0 1
0 2 0 -1 -1 1 2 -2 -1 2 1 -3 1 -1 -1 2 -1 1 1 0 0 0 1 -1
-1 1 2 -1 -1 -1 0 0 -2 1 1 -1 1 0 0 0 1 -2 0 2 -1 0 0 -1
0 1 0 1 -2 1 1 -2 -1 2 0 -1 1 -1 0 1 -1 -1 0 1 -1 1 1 -2
1 0 0 1 0 0 1 0 0 1 1 -1 1 -1 -1 2 0 0 -1 1 0 0 0 0
-1 1 1 -1 -1 1 1 -2 -1 1 0 -1 0 0 1 0 0 -1 0 1 0 0 0 0
0 -1 0 1 -1 0 0 0 0 0 0 1 0 -1 0 0 1 -1 -1 1 0 0 0 0
-1 0 0 0 -1 1 0 -1 0 0 -1 1 -1 0 1 -1 0 -1 0 0 0 0 0 0
0 1 1 0 -1 0 1 0 -1 1 1 -1 1 -1 -1 1 1 -1 -1 2 0 -1 0 0
-2 1 1 -2 -1 0 1 -2 -1 0 0 -1 1 0 0 1 0 0 1 0 1 0 0 0
0 -1 -1 2 -1 0 -1 0 0 0 -1 1 0 0 1 -1 0 -1 0 0 -1 1 1 -2
-1 0 -1 0 -1 1 0 -2 0 0 -1 0 0 0 1 0 -1 0 1 -1 0 1 1 -1
-1 1 0 -2 0 1 1 -2 0 0 0 -1 0 0 0 1 -1 1 1 -1 0 0 0 0
1 -1 -2 2 0 1 -1 0 1 0 -1 1 -1 0 1 -1 -1 0 0 -1 0 0 0 0
1 1 0 0 0 1 1 0 0 1 1 -1 0 -1 -1 1 0 0 -1 1 0 0 0 0
2 -1 -1 2 1 0 -1 2 1 0 0 1 -1 0 0 -1 0 0 -1 0 0 0 0 0
0 1 1 -1 -1 1 2 -2 -1 2 2 -3 1 -1 -1 2 0 0 0 1 0 -1 0 1
-1 1 0 -1 -1 1 0 -2 -1 1 -1 -1 0 0 1 0 -1 0 1 -1 0 0 1 -1
0 0 0 1 -1 1 0 0 0 1 0 1 0 -1 0 0 0 -1 -1 1 -1 0 0 -1
0 0 -1 1 0 1 -1 0 1 0 -2 2 -1 0 1 -1 -1 0 0 -1 -1 1 1 -2
-
HERMITIAN_STRUCTURE
4
24 24
1 0 0 0 0 0 0 0 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 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 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 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 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 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
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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 0 0 0 0 0 0 0 1
24 24
0 1 0 0 0 0 0 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 0 0 0 0 0 0 0
-1 1 1 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 0 1 -1 0 0 0 0 0 0 0 0 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 0 0
0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 -1 1 1 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 -1 0 1 -1 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 -1 1 1 -2 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 -1 0 1 -1 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 -1 1 1 -2 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 -1 0 0 0 0 0 0 0 0
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 0 0 0 0 0 0 -1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 1 -2 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 -1 0 0 0 0
0 0 0 0 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 0 0 0 0 0 0 -1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 1 -2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 -1
24 24
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 -1 -1 2 0 0 0 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 0 0 0 0 0 0 0
0 -1 -1 1 0 0 0 0 0 0 0 0 0 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 0
0 0 0 0 1 -1 -1 2 0 0 0 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 0 0 0
0 0 0 0 0 -1 -1 1 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 1 -1 -1 2 0 0 0 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 0 0 0 0 0 0 0 0 -1 -1 1 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 1 -1 -1 2 0 0 0 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 0 0 0 0 0 0 0 0 -1 -1 1 0 0 0 0 0 0 0 0
0 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 0 0 0 0 0 1 -1 -1 2 0 0 0 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 0 0 0 0 0 0 0 0 -1 -1 1 0 0 0 0
0 0 0 0 0 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 0 0 0 0 0 1 -1 -1 2
0 0 0 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 0 0 0 0 0 0 0 0 -1 -1 1
24 24
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 1 0 -1 0 0 0 0 0 0 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 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 0 0 0 0 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 -1 1 0 -1 0 0 0 0 0 0 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 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 0 0 0 0 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 -1 1 0 -1 0 0 0 0 0 0 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 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 0 0 0 0 -1 -1 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1 0 0 0 0 0 0 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 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 0 0 0 0 -1 -1 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1 0 0 0 0
0 0 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 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 0 0 0 0 -1 -1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1
-
PROPERTIES
Unimodular=1
-
REFERENCES
Bachoc, Nebe: Classification of two genera of 32-dimensional lattices
over the Hurwitz order
-
NOTES
The Niemeier lattice with root system D_4^6
Gram matrix needs to be divided by 2!
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe