The Lattice O22
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 May 17 14:33:03 CEST 2019
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
MINIMAL_NORM
KISSING_NUMBER
GRAM
GROUP_ORDER
GROUP_NAME
GROUP_GENERATORS
INTEGRAL =1
NOTES
LAST_LINE
-
NAME
O22
-
DIMENSION
22
-
DET
3
-
MINIMAL_NORM
3
-
KISSING_NUMBER
2816
-
GRAM
22 22
3 -1 -1 0 0 1 1 0 1 -1 -1 0 -1 -1 1 0 0 0 0 -1 -1 0
-1 3 0 1 0 0 0 1 -1 -1 1 1 1 1 1 -1 -1 1 -1 0 1 -1
-1 0 3 1 0 -1 0 1 1 1 1 1 1 -1 -1 1 1 0 -1 1 1 0
0 1 1 3 1 -1 0 1 0 -1 0 0 1 0 1 1 -1 1 0 1 0 -1
0 0 0 1 3 0 1 -1 0 0 0 0 -1 0 1 1 -1 -1 1 0 0 -1
1 0 -1 -1 0 3 1 0 0 -1 -1 1 0 0 0 -1 -1 -1 0 -1 0 1
1 0 0 0 1 1 3 -1 0 0 -1 0 0 0 1 1 -1 0 -1 0 1 -1
0 1 1 1 -1 0 -1 3 1 -1 1 1 1 0 0 -1 0 1 -1 0 0 0
1 -1 1 0 0 0 0 1 3 0 0 1 0 -1 0 0 1 0 -1 -1 -1 0
-1 -1 1 -1 0 -1 0 -1 0 3 0 0 -1 -1 -1 1 1 0 0 0 0 0
-1 1 1 0 0 -1 -1 1 0 0 3 1 0 0 0 -1 1 0 0 0 1 0
0 1 1 0 0 1 0 1 1 0 1 3 0 -1 0 -1 0 0 -1 -1 0 0
-1 1 1 1 -1 0 0 1 0 -1 0 0 3 1 0 0 0 1 -1 1 1 0
-1 1 -1 0 0 0 0 0 -1 -1 0 -1 1 3 0 0 -1 0 0 1 0 -1
1 1 -1 1 1 0 1 0 0 -1 0 0 0 0 3 0 -1 1 0 -1 0 -1
0 -1 1 1 1 -1 1 -1 0 1 -1 -1 0 0 0 3 0 0 0 1 0 -1
0 -1 1 -1 -1 -1 -1 0 1 1 1 0 0 -1 -1 0 3 0 0 0 0 1
0 1 0 1 -1 -1 0 1 0 0 0 0 1 0 1 0 0 3 -1 0 0 -1
0 -1 -1 0 1 0 -1 -1 -1 0 0 -1 -1 0 0 0 0 -1 3 0 -1 1
-1 0 1 1 0 -1 0 0 -1 0 0 -1 1 1 -1 1 0 0 0 3 1 0
-1 1 1 0 0 0 1 0 -1 0 1 0 1 0 0 0 0 0 -1 1 3 0
0 -1 0 -1 -1 1 -1 0 0 0 0 0 0 -1 -1 -1 1 -1 1 0 0 3
-
GROUP_ORDER
2^17 3^6 5 7 11 = 36787322880
-
GROUP_NAME
(U(6,2)xC2).2
-
GROUP_GENERATORS
3
22 22
1 0 1 0 0 1 -1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0
0 0 2 0 0 1 -1 -1 0 -1 0 -1 -1 0 0 -1 0 1 0 0 0 -1
-1 0 0 0 0 0 1 0 0 -1 0 0 -1 0 0 0 1 0 0 0 0 0
0 1 0 -1 0 1 0 0 0 0 1 -1 0 -1 0 0 0 0 0 1 -1 -1
0 1 1 -1 0 1 0 0 0 0 0 -1 0 -1 0 0 0 0 0 1 -1 -1
1 1 2 -1 0 1 -1 -1 1 0 0 -1 0 0 0 0 -1 1 1 0 0 0
0 -1 3 0 0 2 -1 -1 0 0 0 -1 -1 1 1 -1 0 1 0 0 0 -1
0 1 0 1 -1 1 0 -1 1 0 1 -1 -1 0 0 0 0 0 0 0 0 0
1 0 1 0 0 -1 0 0 0 0 -1 1 -1 2 0 0 0 0 0 -1 1 1
-1 -1 -2 1 0 -1 1 1 0 0 -1 1 0 0 0 0 1 -1 0 0 1 0
-1 0 0 1 -1 0 1 0 0 -1 0 0 -1 0 0 0 1 0 0 0 0 0
1 1 2 -1 0 0 -1 -1 1 -1 -1 0 -1 1 0 0 0 1 1 0 1 0
0 -1 2 0 0 0 0 -1 -1 -1 0 0 -1 1 0 -1 0 1 0 -1 0 0
0 0 -1 0 0 -1 1 0 0 0 1 0 1 -1 -1 0 -1 0 0 0 -1 0
1 -1 3 0 0 2 -2 -1 -1 0 0 -1 -1 1 1 -1 0 1 -1 0 0 -1
-1 0 -2 -1 0 0 1 1 0 0 1 0 1 -2 0 1 0 -1 0 1 -1 -1
0 -1 -1 1 0 -2 1 1 -1 0 -1 2 0 1 0 0 1 -1 0 -1 1 1
0 -1 1 1 -1 1 -1 -1 0 0 0 0 -1 1 1 -1 0 0 0 0 1 -1
0 1 -3 0 0 0 1 1 0 1 1 0 2 -2 -1 1 0 -1 0 1 -1 0
-1 0 -1 0 0 0 1 0 0 0 1 0 0 -1 0 0 0 0 0 1 -1 0
-2 -1 2 1 -1 2 0 -1 0 -1 0 -1 -2 0 1 -1 1 1 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
22 22
-1 0 -3 0 0 0 1 1 0 0 1 0 1 -2 0 1 0 -1 -1 1 -1 0
0 1 1 -1 0 0 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 0 0 0 -1 1 0 0 0 1 0 0 0 1
-1 0 1 -1 0 0 0 0 0 -1 -1 0 -1 0 0 0 0 1 0 0 0 0
0 0 -1 0 1 -2 1 1 0 0 -1 1 0 1 -1 0 0 0 0 -1 1 1
0 0 0 0 1 1 0 0 -1 0 1 -1 1 -1 0 0 0 0 -1 0 -1 0
-1 1 -4 1 0 0 1 1 1 1 1 0 1 -2 -1 1 0 -1 0 1 0 0
0 -1 3 0 0 2 -1 -1 -1 0 0 -1 -1 1 1 -1 0 1 -1 0 -1 0
1 -1 -1 0 1 -1 0 1 -1 1 0 1 1 1 0 0 0 0 -1 0 0 1
0 0 0 1 -1 0 0 0 1 0 0 0 -1 1 0 0 0 0 1 0 1 0
0 -1 1 1 0 -1 1 0 -1 0 -1 1 -1 2 0 -1 1 0 0 -1 0 1
0 0 0 -1 1 -1 1 1 -1 0 0 0 1 0 0 0 0 0 0 0 -1 1
0 0 1 0 0 1 -1 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 1 1 0 0 -1 -1 0 1 -1 0 0 1 0 -1 0 0 0 -1 1 0
-1 0 -3 0 0 -1 1 1 0 0 0 1 1 -1 -1 1 0 -1 0 0 0 0
-1 0 -1 1 -1 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 1 0
1 0 0 0 0 -1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1
-1 0 -1 0 -1 1 0 0 1 0 0 0 0 -1 0 0 0 0 1 1 0 -1
0 0 0 0 0 -1 1 0 0 -1 0 0 0 0 -1 0 0 0 0 -1 0 0
0 1 1 0 0 1 -1 -1 1 0 0 -1 -1 0 0 0 0 1 0 0 0 0
-1 0 0 1 0 1 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0 0
1 0 2 -1 1 1 -1 -1 -1 -1 1 -1 0 0 0 0 0 1 -1 0 -1 0
22 22
-1 1 -3 0 -1 -1 2 1 1 0 1 0 1 -2 -1 1 0 -1 1 1 -1 0
0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 -2 -1 1 -1 1 1 0 0 1 0 1 -1 -1 1 0 0 0 0 -1 1
1 -1 1 0 1 0 -1 0 -1 0 0 0 0 1 0 0 0 1 -1 -1 0 1
0 0 1 -1 0 1 -1 0 0 0 0 -1 0 -1 1 0 0 0 0 1 0 -1
0 0 1 -1 0 0 -1 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0
0 1 -3 -1 1 -1 1 1 0 0 1 0 2 -2 -1 1 0 -1 0 1 -1 0
1 -1 0 -1 2 -2 0 1 -2 0 -1 1 1 1 0 0 0 0 -1 -1 0 1
0 -1 3 1 -1 1 -1 -2 0 -1 -1 0 -2 2 1 -1 0 1 0 -1 1 0
0 0 -1 1 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 -1 0 0 0 0 0 0 0 0 0 0
-1 1 -4 -1 0 -2 2 2 1 0 0 1 1 -2 -1 1 0 -1 1 1 0 0
0 0 -2 0 0 -2 1 1 0 0 0 1 1 -1 -1 0 0 -1 0 0 0 0
0 1 -1 -1 1 -1 1 1 0 0 0 0 1 -1 -1 1 0 0 0 0 -1 1
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 -1 0 0 0 0 0
-1 1 -3 0 0 -2 2 1 1 0 0 1 1 -1 -1 1 0 -1 1 0 0 1
0 0 1 1 0 2 -1 -1 0 0 1 -1 -1 0 0 0 0 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
-1 0 -1 0 -1 1 0 0 1 0 0 0 0 -1 0 0 0 0 1 1 0 -1
0 0 2 0 0 2 -1 -1 0 0 0 -1 -1 0 1 -1 0 1 0 1 0 -1
-
INTEGRAL =1
-
NOTES
orthogonal lattice of minimal vector in O23
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe