The Lattice Delta1
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 13:27:36 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
GRAM
MINIMUM
KISSING_NUMBER
PROPERTIES
NOTES
LAST_LINE
-
NAME
Delta1
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DIMENSION
36
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DET
3^18
-
GRAM
36 36
10 1 -4 -3 0 0 -1 1 -3 -3 -1 2 -3 -3 -2 -1 3 -3 -1 -5 -3 0 -3 3 4 2 1 -4 5 -1 4
0 4 2 3 3
1 8 0 -3 -3 -3 -2 -3 -2 -1 -2 -2 -1 -1 -1 -3 0 -4 1 -4 -4 1 2 0 2 -1 -3 0 0 -2
1 -1 -3 1 0 -1
-4 0 8 -2 -2 2 2 -3 2 0 1 -4 3 0 -1 1 -4 1 -1 -1 2 2 1 -4 1 -1 1 2 0 2 -4 1 -1
1 0 -2
-3 -3 -2 14 -2 -2 -2 -3 5 6 0 -3 4 0 4 -2 -2 4 -4 9 1 -1 -1 5 -8 3 1 4 -3 1 -1
3 4 -2 -1 -2
0 -3 -2 -2 12 3 2 2 -1 2 0 5 -2 5 1 6 5 2 -2 -1 1 -5 0 -4 2 2 -3 3 2 -4 2 -5 0
-3 4 1
0 -3 2 -2 3 10 1 1 3 -3 0 3 -2 1 0 1 -1 2 -2 -1 1 -2 -2 -1 -2 -1 3 1 -2 0 -3 -2
1 3 0 -1
-1 -2 2 -2 2 1 10 -2 -3 1 1 3 0 1 3 6 -4 2 3 -4 2 1 2 -6 3 -1 -3 -1 4 4 -4 -2
-4 -4 -1 -1
1 -3 -3 -3 2 1 -2 12 1 -2 -2 2 -4 2 -2 2 1 -3 4 -2 4 -3 0 4 -2 0 0 -4 -4 0 1 -1
3 0 -1 2
-3 -2 2 5 -1 3 -3 1 14 5 -4 -3 0 1 1 -1 0 0 0 7 3 -5 3 0 -4 4 1 2 -5 -1 -4 0 6
1 3 0
-3 -1 0 6 2 -3 1 -2 5 12 -4 -1 3 2 1 1 2 2 -1 6 4 -2 4 1 -4 6 -2 4 -1 1 -1 2 1
-2 2 -2
-1 -2 1 0 0 0 1 -2 -4 -4 8 1 3 0 -1 -1 0 3 -3 2 -3 4 -4 -3 1 -2 2 1 1 -1 1 2 -1
-1 -3 -1
2 -2 -4 -3 5 3 3 2 -3 -1 1 10 -4 3 2 1 3 0 0 -1 1 -1 -1 -3 1 -1 0 -1 1 -1 2 -3
-3 -1 0 1
-3 -1 3 4 -2 -2 0 -4 0 3 3 -4 8 -2 -1 -2 0 4 -2 3 -1 4 0 -1 -2 0 2 2 0 0 -1 4 1
0 -1 -2
-3 -1 0 0 5 1 1 2 1 2 0 3 -2 8 0 3 1 -1 -1 0 1 -4 2 -2 -1 1 -2 3 -2 -1 1 -4 -3
-1 1 0
-2 -1 -1 4 1 0 3 -2 1 1 -1 2 -1 0 8 1 -3 2 1 2 1 -1 1 -3 -1 -1 -3 1 0 1 -3 -3 0
-4 0 -1
-1 -3 1 -2 6 1 6 2 -1 1 -1 1 -2 3 1 10 -2 0 2 -4 4 -3 2 -4 3 1 -4 0 3 2 -1 -4
-2 -4 2 1
3 0 -4 -2 5 -1 -4 1 0 2 0 3 0 1 -3 -2 10 0 -2 2 -2 -2 0 0 2 2 1 0 1 -5 5 0 2 1
3 3
-3 -4 1 4 2 2 2 -3 0 2 3 0 4 -1 2 0 0 8 -2 5 0 1 -2 -1 -2 0 2 3 0 0 -2 2 1 -2
-2 -2
-1 1 -1 -4 -2 -2 3 4 0 -1 -3 0 -2 -1 1 2 -2 -2 10 -3 1 -1 4 -1 2 -2 -3 -5 -1 2
-3 -2 -2 -1 -1 2
-5 -4 -1 9 -1 -1 -4 -2 7 6 2 -1 3 0 2 -4 2 5 -3 16 2 0 -2 2 -7 4 2 5 -5 -1 -1 4
3 0 -1 -2
-3 -4 2 1 1 1 2 4 3 4 -3 1 -1 1 1 4 -2 0 1 2 10 -1 1 0 -3 1 0 0 -2 4 -2 1 0 -1
0 0
0 1 2 -1 -5 -2 1 -3 -5 -2 4 -1 4 -4 -1 -3 -2 1 -1 0 -1 8 -2 -1 0 -2 2 -1 1 2 0
4 -2 1 -3 -2
-3 2 1 -1 0 -2 2 0 3 4 -4 -1 0 2 1 2 0 -2 4 -2 1 -2 8 -3 1 0 -3 0 -1 1 -2 -2 -3
-1 1 1
3 0 -4 5 -4 -1 -6 4 0 1 -3 -3 -1 -2 -3 -4 0 -1 -1 2 0 -1 -3 14 -6 2 3 -1 -3 1 2
4 4 3 -2 0
4 2 1 -8 2 -2 3 -2 -4 -4 1 1 -2 -1 -1 3 2 -2 2 -7 -3 0 1 -6 12 -1 -2 -3 8 -1 2
-3 -2 -2 3 3
2 -1 -1 3 2 -1 -1 0 4 6 -2 -1 0 1 -1 1 2 0 -2 4 1 -2 0 2 -1 8 -1 2 0 0 1 1 4 0
3 -1
1 -3 1 1 -3 3 -3 0 1 -2 2 0 2 -2 -3 -4 1 2 -3 2 0 2 -3 3 -2 -1 8 -1 -1 1 1 4 2
4 -1 1
-4 0 2 4 3 1 -1 -4 2 4 1 -1 2 3 1 0 0 3 -5 5 0 -1 0 -1 -3 2 -1 8 -2 -2 0 0 -1 0
1 -3
5 0 0 -3 2 -2 4 -4 -5 -1 1 1 0 -2 0 3 1 0 -1 -5 -2 1 -1 -3 8 0 -1 -2 10 0 2 -1
-1 -2 3 2
-1 -2 2 1 -4 0 4 0 -1 1 -1 -1 0 -1 1 2 -5 0 2 -1 4 2 1 1 -1 0 1 -2 0 8 -3 2 -2
0 -3 -1
4 1 -4 -1 2 -3 -4 1 -4 -1 1 2 -1 1 -3 -1 5 -2 -3 -1 -2 0 -2 2 2 1 1 0 2 -3 8 0
0 1 2 2
0 -1 1 3 -5 -2 -2 -1 0 2 2 -3 4 -4 -3 -4 0 2 -2 4 1 4 -2 4 -3 1 4 0 -1 2 0 8 2
2 -3 -1
4 -3 -1 4 0 1 -4 3 6 1 -1 -3 1 -3 0 -2 2 1 -2 3 0 -2 -3 4 -2 4 2 -1 -1 -2 0 2
12 0 3 1
2 1 1 -2 -3 3 -4 0 1 -2 -1 -1 0 -1 -4 -4 1 -2 -1 0 -1 1 -1 3 -2 0 4 0 -2 0 1 2
0 8 1 1
3 0 0 -1 4 0 -1 -1 3 2 -3 0 -1 1 0 2 3 -2 -1 -1 0 -3 1 -2 3 3 -1 1 3 -3 2 -3 3
1 8 3
3 -1 -2 -2 1 -1 -1 2 0 -2 -1 1 -2 0 -1 1 3 -2 2 -2 0 -2 1 0 3 -1 1 -3 2 -1 2 -1
1 1 3 6
-
MINIMUM
6
-
KISSING_NUMBER
2880
-
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