The Lattice Delta2
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 13:27:39 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
GRAM
MINIMUM
KISSING_NUMBER
PROPERTIES
NOTES
LAST_LINE
-
NAME
Delta2
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DIMENSION
36
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DET
3^18
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GRAM
36 36
8 -2 -3 0 -4 3 1 -2 -2 2 2 4 -2 1 3 -3 1 2 -1 -3 2 -2 2 0 -4 -3 3 -1 0 2 -2 -4
4 -2 -1 4
-2 8 4 0 3 1 -2 -3 0 3 1 -3 3 0 1 -1 3 0 2 1 -2 4 -3 -1 -1 3 0 1 -2 -3 1 -1 1
-3 -1 -4
-3 4 12 -2 1 -3 -5 -1 3 3 -4 0 4 -1 -2 5 -1 -3 4 -2 0 3 -3 -2 -2 -2 -1 5 0 1 2
-2 2 -4 4 1
0 0 -2 10 3 -4 4 3 -2 -5 2 3 4 1 3 -3 -3 -3 -2 0 -3 2 0 1 1 0 2 1 -3 -3 -1 1 4
1 3 -4
-4 3 1 3 12 -6 3 3 1 -2 -3 1 2 3 0 -2 -1 -2 3 1 -1 2 -4 3 2 5 -2 4 -5 -1 -3 -2
-3 3 2 0
3 1 -3 -4 -6 16 -3 -3 -3 -1 2 -2 -3 2 2 -1 5 8 -1 3 -4 2 -3 -5 1 -3 -2 -2 2 0
-1 1 -1 -2 -6 -1
1 -2 -5 4 3 -3 12 -1 -4 -3 3 2 0 5 4 -6 0 1 -4 2 -3 -3 5 6 0 -1 4 -4 1 -4 -4 1
-3 1 0 -1
-2 -3 -1 3 3 -3 -1 10 -1 -3 0 1 -2 -2 -1 2 -2 -4 -1 -2 2 2 -2 0 4 3 0 2 -2 0 0
0 1 2 4 0
-2 0 3 -2 1 -3 -4 -1 8 0 -2 -2 0 -3 -4 3 -2 -1 2 1 0 0 0 0 1 0 -1 2 0 2 1 1 -1
1 1 0
2 3 3 -5 -2 -1 -3 -3 0 14 2 -3 0 -3 0 2 0 1 1 0 4 2 0 0 -7 1 0 2 -1 2 1 -4 0 -5
-2 -1
2 1 -4 2 -3 2 3 0 -2 2 12 -3 -1 0 1 -4 0 2 -5 2 -2 -1 2 0 1 1 2 -5 0 -4 0 2 2
-1 -3 -5
4 -3 0 3 1 -2 2 1 -2 -3 -3 12 -1 2 2 -3 -3 -1 2 -3 3 -1 2 3 -1 -5 1 2 1 0 -4 -4
5 1 5 6
-2 3 4 4 2 -3 0 -2 0 0 -1 -1 10 0 1 -1 -1 -3 1 2 -1 2 -1 -1 -2 0 -3 4 -1 -2 0 0
0 0 2 -2
1 0 -1 1 3 2 5 -2 -3 -3 0 2 0 10 1 -4 2 3 -1 0 -4 -2 -3 0 1 -3 0 -1 -1 0 -4 -1
-3 2 -1 3
3 1 -2 3 0 2 4 -1 -4 0 1 2 1 1 8 -2 1 0 -1 1 0 2 3 1 -2 -2 4 1 1 -1 -3 -2 1 -3
-1 -2
-3 -1 5 -3 -2 -1 -6 2 3 2 -4 -3 -1 -4 -2 12 -4 -3 4 0 1 2 0 -4 0 -2 -1 4 0 3 2
0 1 -1 2 -2
1 3 -1 -3 -1 5 0 -2 -2 0 0 -3 -1 2 1 -4 10 1 -2 0 -1 0 -1 -1 1 3 2 -4 2 -1 1 -1
-3 -2 -2 2
2 0 -3 -3 -2 8 1 -4 -1 1 2 -1 -3 3 0 -3 1 10 -1 1 -3 -1 -2 0 -1 -1 -1 -3 0 2 -1
1 -3 -1 -6 -1
-1 2 4 -2 3 -1 -4 -1 2 1 -5 2 1 -1 -1 4 -2 -1 8 0 2 1 -3 -2 -1 -1 -3 5 -2 2 0
-2 2 1 2 3
-3 1 -2 0 1 3 2 -2 1 0 2 -3 2 0 1 0 0 1 0 10 -3 2 1 0 2 -2 -2 1 2 -4 -3 3 -5 1
-1 -4
2 -2 0 -3 -1 -4 -3 2 0 4 -2 3 -1 -4 0 1 -1 -3 2 -3 10 -2 2 1 -2 1 0 2 1 3 0 -3
1 0 2 5
-2 4 3 2 2 2 -3 2 0 2 -1 -1 2 -2 2 2 0 -1 1 2 -2 8 -2 -1 0 0 0 4 -1 -2 -1 -1 1
-3 2 -5
2 -3 -3 0 -4 -3 5 -2 0 0 2 2 -1 -3 3 0 -1 -2 -3 1 2 -2 12 5 -1 -3 5 -4 6 -3 -2
0 0 -1 2 -2
0 -1 -2 1 3 -5 6 0 0 0 0 3 -1 0 1 -4 -1 0 -2 0 1 -1 5 8 -1 1 3 -2 2 -3 -3 -1 -2
0 2 0
-4 -1 -2 1 2 1 0 4 1 -7 1 -1 -2 1 -2 0 1 -1 -1 2 -2 0 -1 -1 8 1 -1 -2 1 -2 0 4
-2 4 1 -1
-3 3 -2 0 5 -3 -1 3 0 1 1 -5 0 -3 -2 -2 3 -1 -1 -2 1 0 -3 1 1 12 -2 -2 -4 0 4 0
-2 1 -3 -2
3 0 -1 2 -2 -2 4 0 -1 0 2 1 -3 0 4 -1 2 -1 -3 -2 0 0 5 3 -1 -2 10 -3 2 -2 -1 -1
2 -4 2 -2
-1 1 5 1 4 -2 -4 2 2 2 -5 2 4 -1 1 4 -4 -3 5 1 2 4 -4 -2 -2 -2 -3 10 -3 2 -2 -3
1 0 3 1
0 -2 0 -3 -5 2 1 -2 0 -1 0 1 -1 -1 1 0 2 0 -2 2 1 -1 6 2 1 -4 2 -3 8 -2 -1 1 -2
-1 1 1
2 -3 1 -3 -1 0 -4 0 2 2 -4 0 -2 0 -1 3 -1 2 2 -4 3 -2 -3 -3 -2 0 -2 2 -2 10 2
-2 -1 0 -3 5
-2 1 2 -1 -3 -1 -4 0 1 1 0 -4 0 -4 -3 2 1 -1 0 -3 0 -1 -2 -3 0 4 -1 -2 -1 2 8 3
2 -1 -2 -1
-4 -1 -2 1 -2 1 1 0 1 -4 2 -4 0 -1 -2 0 -1 1 -2 3 -3 -1 0 -1 4 0 -1 -3 1 -2 3 8
-2 2 -2 -4
4 1 2 4 -3 -1 -3 1 -1 0 2 5 0 -3 1 1 -3 -3 2 -5 1 1 0 -2 -2 -2 2 1 -2 -1 2 -2
12 -2 3 0
-2 -3 -4 1 3 -2 1 2 1 -5 -1 1 0 2 -3 -1 -2 -1 1 1 0 -3 -1 0 4 1 -4 0 -1 0 -1 2
-2 8 0 2
-1 -1 4 3 2 -6 0 4 1 -2 -3 5 2 -1 -1 2 -2 -6 2 -1 2 2 2 2 1 -3 2 3 1 -3 -2 -2 3
0 10 2
4 -4 1 -4 0 -1 -1 0 0 -1 -5 6 -2 3 -2 -2 2 -1 3 -4 5 -5 -2 0 -1 -2 -2 1 1 5 -1
-4 0 2 2 14
-
MINIMUM
6
-
KISSING_NUMBER
576
-
PROPERTIES
modular = 3
-
NOTES
Constructed by G. Nebe applying the Turyn construction to the Coxeter Todd lattice. This yields in total five 3-modular lattices of dimension 36
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe