The Lattice Delta3
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 13:27:40 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
GRAM
MINIMUM
KISSING_NUMBER
PROPERTIES
NOTES
LAST_LINE
-
NAME
Delta3
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DIMENSION
36
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DET
3^18
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GRAM
36 36
10 -3 -3 4 -3 0 4 -1 -2 -1 4 2 1 3 -2 2 0 2 -2 -1 -4 -2 -4 -4 -3 3 3 -1 2 1 -3
-5 -4 0 0 3
-3 12 -2 2 -1 4 -6 5 -4 4 -4 -4 -1 -2 -3 2 -4 -5 -4 2 -1 1 -2 3 0 3 -5 -2 1 1
-4 3 6 5 4 -5
-3 -2 12 3 -2 1 5 3 3 1 -4 3 0 -1 2 3 2 -2 3 3 1 1 -3 3 -1 -7 -5 0 3 -4 -1 0 -1
2 -6 -1
4 2 3 12 -2 4 1 2 -4 3 -2 0 -2 3 -5 6 -2 0 -2 1 -4 -3 -7 2 -3 -3 -4 -2 1 -2 -7
-5 -2 4 -3 1
-3 -1 -2 -2 8 -1 -2 -4 3 1 0 1 0 0 -1 -1 -2 3 3 -2 4 1 1 0 1 0 0 2 -5 1 2 3 2
-1 0 0
0 4 1 4 -1 8 1 4 -1 4 -4 -2 -3 0 0 4 -2 -4 -1 0 1 1 -2 -1 0 0 -2 -3 1 0 -3 -2 3
1 2 -1
4 -6 5 1 -2 1 12 -2 2 -1 -1 4 0 0 2 1 4 2 0 2 -1 2 -4 -2 -2 -1 1 -2 2 -3 0 -1
-4 0 -3 3
-1 5 3 2 -4 4 -2 10 -1 4 -1 -3 1 1 1 1 -1 -6 1 0 -2 2 -2 2 0 -2 -3 -2 5 0 -4 0
4 1 2 -2
-2 -4 3 -4 3 -1 2 -1 8 -2 1 1 2 -2 2 -2 1 2 4 0 3 1 2 0 2 -3 2 2 -1 0 2 2 2 -3
-3 -1
-1 4 1 3 1 4 -1 4 -2 8 -1 0 -1 1 1 3 -2 -3 0 -1 0 3 -2 1 0 0 -4 -2 1 -1 -3 2 3
3 3 0
4 -4 -4 -2 0 -4 -1 -1 1 -1 10 1 2 1 -1 -3 0 3 1 -4 -1 1 3 -2 0 2 5 1 2 2 -1 -1
-1 -2 2 4
2 -4 3 0 1 -2 4 -3 1 0 1 8 0 1 0 2 2 1 2 0 2 2 -1 -3 0 1 0 0 1 0 2 -1 -4 2 -1
2
1 -1 0 -2 0 -3 0 1 2 -1 2 0 6 -1 0 -2 0 1 0 0 -2 0 0 1 -1 0 2 0 0 0 -1 2 -1 -1
-2 -2
3 -2 -1 3 0 0 0 1 -2 1 1 1 -1 6 -1 0 1 0 2 -1 -1 -1 -3 -1 0 0 0 1 1 1 -1 -2 -1
0 0 2
-2 -3 2 -5 -1 0 2 1 2 1 -1 0 0 -1 8 -1 2 -1 2 0 2 2 3 -1 1 -1 1 0 1 -1 4 2 0 -3
1 0
2 2 3 6 -1 4 1 1 -2 3 -3 2 -2 0 -1 8 -2 -2 -1 0 0 0 -4 0 -1 0 -3 -1 1 -1 -3 -3
-1 2 -1 -1
0 -4 2 -2 -2 -2 4 -1 1 -2 0 2 0 1 2 -2 6 1 1 2 -1 1 0 0 1 -1 1 0 1 -1 3 0 -3 -1
-1 2
2 -5 -2 0 3 -4 2 -6 2 -3 3 1 1 0 -1 -2 1 8 0 0 -1 -2 0 0 -1 -1 3 1 -3 0 1 0 -3
-2 -3 2
-2 -4 3 -2 3 -1 0 1 4 0 1 2 0 2 2 -1 1 0 8 -2 3 2 0 0 1 -3 -1 2 1 0 2 0 0 -3 -1
1
-1 2 3 1 -2 0 2 0 0 -1 -4 0 0 -1 0 0 2 0 -2 6 -2 -1 -3 2 0 -1 -2 0 0 -2 0 1 0 3
-3 -2
-4 -1 1 -4 4 1 -1 -2 3 0 -1 2 -2 -1 2 0 -1 -1 3 -2 8 2 4 -2 2 1 0 1 -1 2 3 2 2
-1 1 -1
-2 1 1 -3 1 1 2 2 1 3 1 2 0 -1 2 0 1 -2 2 -1 2 8 1 0 1 2 -1 -1 2 -1 0 4 2 1 4
0
-4 -2 -3 -7 1 -2 -4 -2 2 -2 3 -1 0 -3 3 -4 0 0 0 -3 4 1 12 -2 3 1 3 0 -2 1 4 2
0 -4 2 1
-4 3 3 2 0 -1 -2 2 0 1 -2 -3 1 -1 -1 0 0 0 0 2 -2 0 -2 8 0 -3 -4 1 0 -2 -2 3 2
1 -3 -3
-3 0 -1 -3 1 0 -2 0 2 0 0 0 -1 0 1 -1 1 -1 1 0 2 1 3 0 6 0 1 1 -1 0 2 2 2 -1 1
0
3 3 -7 -3 0 0 -1 -2 -3 0 2 1 0 0 -1 0 -1 -1 -3 -1 1 2 1 -3 0 10 3 -1 1 3 0 1 0
1 5 -1
3 -5 -5 -4 0 -2 1 -3 2 -4 5 0 2 0 1 -3 1 3 -1 -2 0 -1 3 -4 1 3 10 1 -1 3 2 -2
-1 -4 1 1
-1 -2 0 -2 2 -3 -2 -2 2 -2 1 0 0 1 0 -1 0 1 2 0 1 -1 0 1 1 -1 1 6 -2 1 3 0 2 -1
-2 -1
2 1 3 1 -5 1 2 5 -1 1 2 1 0 1 1 1 1 -3 1 0 -1 2 -2 0 -1 1 -1 -2 8 0 -3 -1 0 1 1
0
1 1 -4 -2 1 0 -3 0 0 -1 2 0 0 1 -1 -1 -1 0 0 -2 2 -1 1 -2 0 3 3 1 0 6 1 -1 2 -1
2 -1
-3 -4 -1 -7 2 -3 0 -4 2 -3 -1 2 -1 -1 4 -3 3 1 2 0 3 0 4 -2 2 0 2 3 -3 1 10 0
-1 -3 1 1
-5 3 0 -5 3 -2 -1 0 2 2 -1 -1 2 -2 2 -3 0 0 0 1 2 4 2 3 2 1 -2 0 -1 -1 0 10 4 1
1 -3
-4 6 -1 -2 2 3 -4 4 2 3 -1 -4 -1 -1 0 -1 -3 -3 0 0 2 2 0 2 2 0 -1 2 0 2 -1 4 10
1 3 -4
0 5 2 4 -1 1 0 1 -3 3 -2 2 -1 0 -3 2 -1 -2 -3 3 -1 1 -4 1 -1 1 -4 -1 1 -1 -3 1
1 8 1 -1
0 4 -6 -3 0 2 -3 2 -3 3 2 -1 -2 0 1 -1 -1 -3 -1 -3 1 4 2 -3 1 5 1 -2 1 2 1 1 3
1 10 1
3 -5 -1 1 0 -1 3 -2 -1 0 4 2 -2 2 0 -1 2 2 1 -2 -1 0 1 -3 0 -1 1 -1 0 -1 1 -3
-4 -1 1 8
-
MINIMUM
6
-
KISSING_NUMBER
12096
-
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