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 13:21:01 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DETERMINANT
MINIMAL_NORM
KISSING_NUMBER
DENSITY
HERMITE_NUMBER
GROUP_ORDER
GRAM
BASIS
ROOT_SYSTEM
NOTES
LAST_LINE

• NAME
  N(8A3)
  

• DIMENSION
  24
  

• DETERMINANT
  1
  

• MINIMAL_NORM
  2
  

• KISSING_NUMBER
  96
  

• DENSITY
  .596E-07
  

• HERMITE_NUMBER
  2
  

• GROUP_ORDER
  2^31 * 3^9 * 7
  

• GRAM
  24 0
  2
  1 2
  -1 -1 2
  0 0 0 2
  0 0 0 0 2
  0 0 0 0 0 2
  0 0 0 0 0 0 2
  0 0 0 0 0 0 0 2
  0 0 0 0 0 0 0 -1 2
  0 0 0 0 0 0 0 0 -1 2
  0 0 0 0 0 0 0 0 0 0 2
  0 0 0 0 0 0 0 0 0 0 1 2
  0 0 0 0 0 0 0 0 0 0 -1 0 2
  0 -1 1 0 0 1 0 1 -1 1 -1 -1 1 4
  1 0 -1 -1 0 0 1 -1 1 0 1 1 0 -1 4
  0 0 1 -1 0 0 0 0 1 -1 -1 0 0 0 0 4
  0 0 1 0 -1 -1 0 0 1 -1 -1 -1 0 0 -1 2 4
  1 1 -1 1 0 -1 1 0 0 0 -1 -1 1 0 0 -1 1 4
  1 1 -1 -1 0 1 0 0 -1 1 1 0 -1 0 1 -1 -2 -1 4
  1 1 -1 0 0 1 1 0 1 -1 -1 0 1 0 1 1 0 1 0 4
  1 1 -1 0 0 1 -1 1 -1 0 1 1 0 0 0 -1 -2 -1 2 0 4
  0 0 0 1 0 -1 0 -1 1 -1 -1 -1 0 -1 -1 0 2 2 -2 0 -2 4
  0 0 0 1 0 -1 0 -1 1 -1 -1 -1 0 -1 -1 0 2 2 -2 0 -2 3 4
  0 0 0 0 1 -1 1 -1 1 -1 1 1 0 -2 2 0 0 1 -1 0 -1 1 1 4
  

• BASIS
  24 32
  .100000000000E+01 .000000000000E+00 -.100000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00
  .000000000000E+00 .100000000000E+01 -.100000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00
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  -.100000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
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  .000000000000E+00 .000000000000E+00 .000000000000E+00
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  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
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  -.500000000000E+00 .500000000000E+00 .500000000000E+00
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  .000000000000E+00 .000000000000E+00
  .500000000000E+00 -.500000000000E+00 -.500000000000E+00
  .500000000000E+00 -.250000000000E+00 -.250000000000E+00
  .750000000000E+00 -.250000000000E+00 .000000000000E+00
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  .250000000000E+00 .250000000000E+00 -.250000000000E+00
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  .250000000000E+00 -.750000000000E+00
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  -.750000000000E+00 .000000000000E+00 .000000000000E+00
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  .500000000000E+00 .500000000000E+00 -.500000000000E+00
  -.250000000000E+00 -.250000000000E+00 .750000000000E+00
  -.250000000000E+00 .000000000000E+00 .000000000000E+00
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  .250000000000E+00 -.750000000000E+00 .250000000000E+00
  -.750000000000E+00 .250000000000E+00 .250000000000E+00
  .250000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00
  .250000000000E+00 .250000000000E+00 -.750000000000E+00
  .250000000000E+00 .250000000000E+00 .250000000000E+00
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  -.500000000000E+00 .500000000000E+00 .500000000000E+00
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  .250000000000E+00 -.500000000000E+00 -.500000000000E+00
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  .250000000000E+00 -.750000000000E+00 .250000000000E+00
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  .250000000000E+00 .000000000000E+00 .000000000000E+00
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  .750000000000E+00 -.250000000000E+00 -.250000000000E+00
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  .000000000000E+00 .250000000000E+00 .250000000000E+00
  -.750000000000E+00 .250000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  -.250000000000E+00 -.250000000000E+00 .750000000000E+00
  -.250000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 -.500000000000E+00
  .500000000000E+00 -.500000000000E+00 .500000000000E+00
  -.750000000000E+00 .250000000000E+00 .250000000000E+00
  .250000000000E+00 .250000000000E+00 -.750000000000E+00
  .250000000000E+00 .250000000000E+00
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  .000000000000E+00 .250000000000E+00 .250000000000E+00
  -.750000000000E+00 .250000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  -.250000000000E+00 -.250000000000E+00 .750000000000E+00
  -.250000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 -.500000000000E+00
  .500000000000E+00 -.500000000000E+00 .500000000000E+00
  -.750000000000E+00 .250000000000E+00 .250000000000E+00
  .250000000000E+00 -.750000000000E+00 .250000000000E+00
  .250000000000E+00 .250000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .750000000000E+00
  -.250000000000E+00 -.250000000000E+00 -.250000000000E+00
  -.250000000000E+00 -.250000000000E+00 .750000000000E+00
  -.250000000000E+00 .250000000000E+00 -.750000000000E+00
  .250000000000E+00 .250000000000E+00 -.500000000000E+00
  .500000000000E+00 -.500000000000E+00 .500000000000E+00
  .750000000000E+00 -.250000000000E+00 -.250000000000E+00
  -.250000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00
  

• ROOT_SYSTEM
  8A3
  

• NOTES
  One of the 24 even unimodular lattices in dimension 24 (the Niemeier lattices)
  

• LAST_LINE
  

  ---

  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe