The Lattice O_10
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 13:21:15 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM
GROUP_ORDER
GROUP_GENERATORS
PROPERTIES
SIMILARITY
REFERENCES
NOTES
LAST_LINE
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NAME
O_10
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DIMENSION
10
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GRAM
10 10
3 -1 -1 -1 -1 1 0 -1 -1 1
-1 3 -1 1 0 -1 1 1 -1 1
-1 -1 3 1 0 -1 -1 0 1 -1
-1 1 1 3 -1 -1 -1 1 1 0
-1 0 0 -1 3 -1 1 -1 0 -1
1 -1 -1 -1 -1 3 -1 0 0 1
0 1 -1 -1 1 -1 3 -1 -1 0
-1 1 0 1 -1 0 -1 3 1 1
-1 -1 1 1 0 0 -1 1 3 -1
1 1 -1 0 -1 1 0 1 -1 3
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GROUP_ORDER
103680
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GROUP_GENERATORS
10
0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 -1 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 -1 0 0 0 0
0 1 0 -1 0 0 -1 0 0 0
0 0 0 0 0 0 1 0 0 0
1 1 1 0 0 1 0 0 0 -1
1 0 0 0 0 0 0 1 0 -1
1 1 1 0 1 1 0 0 0 0
10
1 1 1 0 0 1 1 1 0 -1
-1 -1 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0 0 0
0 1 0 -1 0 -1 -1 -1 1 1
0 0 0 0 0 0 0 1 -1 -1
0 0 0 0 0 0 0 0 0 1
-1 -1 -1 0 0 0 0 0 0 0
0 -1 -1 0 0 -1 0 0 0 0
-1 0 0 -1 -1 0 0 0 0 0
10
1 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 1 1 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0 0 0
0 -1 -1 1 0 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
-1 -1 0 0 0 0 0 0 0 1
1 1 0 0 0 0 0 0 1 0
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PROPERTIES
INTEGRAL=1
MODULAR=3
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SIMILARITY
10
0 2 0 -2 -1 -1 -1 -2 3 1
2 1 1 1 1 2 1 2 -1 -3
0 -2 0 1 1 0 1 2 -1 1
1 -1 1 2 1 2 3 2 -1 -1
0 -1 -1 2 1 0 -1 0 -1 0
-2 0 -1 -2 -3 -2 -1 -2 1 1
1 2 1 0 1 2 -1 0 0 -1
1 1 1 0 0 0 1 1 -1 -1
-1 -1 -1 1 0 0 1 0 -1 1
2 2 1 -1 -1 0 0 0 1 -1
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REFERENCES
E. M. Rains and N. J. A. Sloane,
The Shadow Theory of Modular and Unimodular Lattices,
J. Number Theory, 73 (1998), pp. 359-389;
http://neilsloane.com/doc/shad.pdf or shad.ps
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NOTES
The shorter Coxeter-Todd lattice.
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe