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 13:27:42 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
GRAM
MINIMUM
KISSING_NUMBER
PROPERTIES
NOTES
LAST_LINE

• NAME
  Delta4
  

• DIMENSION
  36
  

• DET
  3^18
  

• GRAM
  36 36
  6 -3 1 0 2 0 1 0 1 0 -2 0 -1 0 0 -2 1 -1 2 -3 2 1 2 -2 1 -2 0 -3 0 -3 -2 2 -1
  -2 2 -1
  -3 10 3 0 -2 0 2 1 -4 1 1 2 -1 4 -1 -3 -4 -3 2 4 0 3 -1 -3 2 -2 3 4 -4 -2 2 3 1
  1 -5 3
  1 3 16 -6 -1 -4 5 -5 -1 7 1 -4 5 -4 -7 -1 -4 2 -1 -3 3 7 -6 -2 8 4 -1 3 -5 -9
  -1 -4 -4 4 -8 -5
  0 0 -6 18 8 9 -9 10 3 -1 3 1 3 7 4 2 0 0 2 2 -4 1 6 7 -8 4 -3 -4 7 4 -4 0 -2 5
  9 -4
  2 -2 -1 8 14 2 -6 3 -2 2 0 0 3 2 -3 1 -4 -1 -2 3 -4 -1 6 2 0 2 2 -3 2 1 -1 0 1
  5 2 -7
  0 0 -4 9 2 12 -2 7 0 -3 0 4 0 7 3 4 0 2 5 1 -1 1 4 4 -5 2 -4 0 3 0 0 3 -4 2 3
  -4
  1 2 5 -9 -6 -2 12 -2 -4 -2 -4 3 -1 -4 -4 1 -2 -2 3 -1 5 3 -4 -4 2 -2 -2 3 -2 -6
  3 2 0 -2 -4 2
  0 1 -5 10 3 7 -2 12 -2 -3 1 3 0 5 2 3 -2 -1 5 2 1 0 5 5 -4 2 -3 -1 4 2 1 4 -2 3
  6 -1
  1 -4 -1 3 -2 0 -4 -2 12 3 4 -2 4 1 2 1 6 4 -4 -6 -1 -1 0 1 -5 3 -3 -1 5 3 -3 -6
  -4 -3 6 -2
  0 1 7 -1 2 -3 -2 -3 3 10 5 -2 6 -1 -2 -1 0 3 -2 0 -2 2 -2 -1 5 4 1 0 -2 -1 -2
  -5 -4 2 -4 -3
  -2 1 1 3 0 0 -4 1 4 5 8 -2 3 3 2 1 0 2 -1 0 -3 0 0 1 1 5 -1 1 1 1 -1 -4 -2 0 2
  0
  0 2 -4 1 0 4 3 3 -2 -2 -2 8 -1 2 1 2 -1 -2 4 3 0 0 2 -1 -2 -2 0 0 2 0 1 4 0 -2
  1 0
  -1 -1 5 3 3 0 -1 0 4 6 3 -1 10 -2 -2 3 1 3 -3 -1 -2 2 -1 3 0 6 -3 1 3 0 -2 -6
  -3 3 1 -5
  0 4 -4 7 2 7 -4 5 1 -1 3 2 -2 12 2 -1 -1 -1 2 2 -1 -1 5 -1 -3 0 1 2 0 1 2 3 -1
  -1 2 1
  0 -1 -7 4 -3 3 -4 2 2 -2 2 1 -2 2 10 -1 4 0 3 0 -2 -1 2 2 -2 -1 -1 -3 1 4 -3 2
  1 -4 4 5
  -2 -3 -1 2 1 4 1 3 1 -1 1 2 3 -1 -1 8 -1 3 0 -1 0 0 1 4 -3 5 -4 1 4 1 1 -2 -2 2
  3 -4
  1 -4 -4 0 -4 0 -2 -2 6 0 0 -1 1 -1 4 -1 10 1 -1 -4 -1 -3 -1 1 -4 -1 -1 -2 2 3
  -3 -2 -2 -4 4 1
  -1 -3 2 0 -1 2 -2 -1 4 3 2 -2 3 -1 0 3 1 8 -1 -3 0 0 -1 2 0 3 -3 1 0 2 -1 -3 -4
  2 -2 -3
  2 2 -1 2 -2 5 3 5 -4 -2 -1 4 -3 2 3 0 -1 -1 10 1 1 2 1 0 1 -1 -2 -1 -1 -2 -1 6
  -1 -1 1 1
  -3 4 -3 2 3 1 -1 2 -6 0 0 3 -1 2 0 -1 -4 -3 1 10 -3 -1 1 0 1 -1 3 0 -1 2 2 2 4
  3 -2 2
  2 0 3 -4 -4 -1 5 1 -1 -2 -3 0 -2 -1 -2 0 -1 0 1 -3 8 2 -1 -1 1 -1 -1 1 -2 -2 1
  2 -2 -1 -1 2
  1 3 7 1 -1 1 3 0 -1 2 0 0 2 -1 -1 0 -3 0 2 -1 2 8 -2 0 2 2 -2 0 -1 -6 -2 0 -3 3
  -3 -1
  2 -1 -6 6 6 4 -4 5 0 -2 0 2 -1 5 2 1 -1 -1 1 1 -1 -2 8 1 -2 -1 1 -1 2 3 1 4 1
  -1 4 -1
  -2 -3 -2 7 2 4 -4 5 1 -1 1 -1 3 -1 2 4 1 2 0 0 -1 0 1 8 -3 5 -4 -2 4 3 -2 -2 -2
  4 4 -4
  1 2 8 -8 0 -5 2 -4 -5 5 1 -2 0 -3 -2 -3 -4 0 1 1 1 2 -2 -3 12 0 3 2 -7 -5 1 1 0
  0 -8 0
  -2 -2 4 4 2 2 -2 2 3 4 5 -2 6 0 -1 5 -1 3 -1 -1 -1 2 -1 5 0 10 -5 0 3 0 -1 -6
  -4 4 2 -5
  0 3 -1 -3 2 -4 -2 -3 -3 1 -1 0 -3 1 -1 -4 -1 -3 -2 3 -1 -2 1 -4 3 -5 8 0 -4 1 1
  2 4 -1 -3 3
  -3 4 3 -4 -3 0 3 -1 -1 0 1 0 1 2 -3 1 -2 1 -1 0 1 0 -1 -2 2 0 0 8 -2 -2 4 0 0
  -1 -3 0
  0 -4 -5 7 2 3 -2 4 5 -2 1 2 3 0 1 4 2 0 -1 -1 -2 -1 2 4 -7 3 -4 -2 10 2 -1 -3
  -1 0 9 -3
  -3 -2 -9 4 1 0 -6 2 3 -1 1 0 0 1 4 1 3 2 -2 2 -2 -6 3 3 -5 0 1 -2 2 12 0 -1 3
  -1 4 3
  -2 2 -1 -4 -1 0 3 1 -3 -2 -1 1 -2 2 -3 1 -3 -1 -1 2 1 -2 1 -2 1 -1 1 4 -1 0 8 2
  1 0 -3 1
  2 3 -4 0 0 3 2 4 -6 -5 -4 4 -6 3 2 -2 -2 -3 6 2 2 0 4 -2 1 -6 2 0 -3 -1 2 10 2
  -2 -1 3
  -1 1 -4 -2 1 -4 0 -2 -4 -4 -2 0 -3 -1 1 -2 -2 -4 -1 4 -2 -3 1 -2 0 -4 4 0 -1 3
  1 2 10 -2 1 5
  -2 1 4 5 5 2 -2 3 -3 2 0 -2 3 -1 -4 2 -4 2 -1 3 -1 3 -1 4 0 4 -1 -1 0 -1 0 -2
  -2 10 -3 -5
  2 -5 -8 9 2 3 -4 6 6 -4 2 1 1 2 4 3 4 -2 1 -2 -1 -3 4 4 -8 2 -3 -3 9 4 -3 -1 1
  -3 16 -1
  -1 3 -5 -4 -7 -4 2 -1 -2 -3 0 0 -5 1 5 -4 1 -3 1 2 2 -1 -1 -4 0 -5 3 0 -3 3 1 3
  5 -5 -1 14
  
  

• MINIMUM
  6
  

• KISSING_NUMBER
  2016
  

• 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
  

• LAST_LINE
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe