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 13:27:43 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
GRAM
MINIMUM
KISSING_NUMBER
PROPERTIES
NOTES
LAST_LINE

• NAME
  Delta5
  

• DIMENSION
  36
  

• DET
  3^18
  

• GRAM
  36 36
  10 -1 -4 3 3 -4 -4 4 -3 0 -3 0 -1 -4 -3 0 -4 -4 -2 3 2 -2 -1 -4 5 -2 -3 -3 -4 3
  3 3 -2 3 -5 0
  -1 10 0 -1 -4 4 -4 -5 -1 -1 0 1 2 0 -2 1 0 2 4 1 -5 1 2 4 -5 -4 2 -4 -2 0 0 4 0
  1 3 -4
  -4 0 10 1 1 1 1 -4 0 4 4 4 3 4 -2 -4 4 -1 3 -5 -2 -1 -3 1 -6 1 1 2 -1 1 -1 -5
  -3 -4 4 3
  3 -1 1 8 1 -2 1 -2 -3 -2 -3 1 1 0 -4 -4 1 -3 -2 2 -2 -2 1 0 3 1 -2 1 1 -1 -1 1
  -2 3 -2 2
  3 -4 1 1 10 -4 -1 1 -4 5 -2 1 -4 -1 -4 -1 0 0 -4 0 4 1 -1 -5 1 3 1 4 -2 3 1 0
  -1 0 0 -1
  -4 4 1 -2 -4 10 1 -1 3 -4 2 -1 3 4 1 1 3 0 0 -2 -4 -2 3 6 -2 2 1 -3 -1 -4 1 0 0
  0 1 0
  -4 -4 1 1 -1 1 10 2 2 -4 0 -1 2 2 0 -3 1 -2 -1 -3 -1 -3 1 0 2 1 1 1 2 -2 -1 -2
  2 0 -2 0
  4 -5 -4 -2 1 -1 2 12 1 -1 -1 -3 0 0 1 2 -3 -1 -4 -1 3 -3 0 -4 3 0 0 -2 -3 2 3
  -1 -1 -1 -4 -1
  -3 -1 0 -3 -4 3 2 1 10 -4 5 1 3 1 5 3 1 0 4 -3 -1 -1 -3 5 -2 3 -3 1 2 -2 -2 -3
  -1 0 1 1
  0 -1 4 -2 5 -4 -4 -1 -4 12 -1 3 -4 -1 -2 1 1 4 0 -2 3 4 -2 -5 -4 -1 1 2 -1 3 1
  -1 1 -3 5 2
  -3 0 4 -3 -2 2 0 -1 5 -1 8 1 4 1 4 -1 1 0 4 -4 -1 0 -4 2 -3 0 -1 1 0 1 -2 -5 -2
  -2 1 1
  0 1 4 1 1 -1 -1 -3 1 3 1 6 0 0 -2 0 2 -1 2 -1 -2 -1 -2 0 -3 -1 0 0 -1 0 0 -1 -1
  0 3 2
  -1 2 3 1 -4 3 2 0 3 -4 4 0 10 3 0 -2 1 -4 2 -3 -4 -4 0 3 0 1 -1 -1 0 2 -1 -3 -1
  -2 1 -1
  -4 0 4 0 -1 4 2 0 1 -1 1 0 3 8 1 0 4 -1 -1 -2 -2 -2 0 3 -4 2 1 2 0 -2 -1 -3 -1
  -4 3 2
  -3 -2 -2 -4 -4 1 0 1 5 -2 4 -2 0 1 10 2 0 2 2 0 1 3 -2 1 -1 -1 -1 2 3 -3 -2 -2
  2 -1 0 3
  0 1 -4 -4 -1 1 -3 2 3 1 -1 0 -2 0 2 8 0 2 0 2 1 1 0 2 0 1 -1 -1 0 -1 1 1 2 0 3
  -1
  -4 0 4 1 0 3 1 -3 1 1 1 2 1 4 0 0 6 1 0 -1 -2 -1 0 2 -2 2 0 3 1 -2 -2 -3 0 -2 4
  3
  -4 2 -1 -3 0 0 -2 -1 0 4 0 -1 -4 -1 2 2 1 10 0 0 0 5 1 -1 -5 0 1 2 2 -1 -3 1 2
  0 3 -1
  -2 4 3 -2 -4 0 -1 -4 4 0 4 2 2 -1 2 0 0 0 10 -2 -2 2 -4 3 -5 -4 -1 0 -1 1 -2 -1
  -2 -1 3 0
  3 1 -5 2 0 -2 -3 -1 -3 -2 -4 -1 -3 -2 0 2 -1 0 -2 8 1 1 2 -1 4 -1 -1 -1 0 -1 0
  4 2 2 -1 0
  2 -5 -2 -2 4 -4 -1 3 -1 3 -1 -2 -4 -2 1 1 -2 0 -2 1 8 2 -2 -4 2 2 0 2 0 2 1 -1
  1 -1 -1 0
  -2 1 -1 -2 1 -2 -3 -3 -1 4 0 -1 -4 -2 3 1 -1 5 2 1 2 8 0 -1 -3 -1 1 3 2 -1 -2 2
  2 1 3 0
  -1 2 -3 1 -1 3 1 0 -3 -2 -4 -2 0 0 -2 0 0 1 -4 2 -2 0 8 1 3 1 3 -2 1 -2 1 3 2 2
  0 -2
  -4 4 1 0 -5 6 0 -4 5 -5 2 0 3 3 1 2 2 -1 3 -1 -4 -1 1 10 -2 3 -1 -1 2 -3 -1 0
  -2 1 2 -1
  5 -5 -6 3 1 -2 2 3 -2 -4 -3 -3 0 -4 -1 0 -2 -5 -5 4 2 -3 3 -2 14 2 -3 -1 2 1 2
  1 2 3 -6 1
  -2 -4 1 1 3 2 1 0 3 -1 0 -1 1 2 -1 1 2 0 -4 -1 2 -1 1 3 2 12 -2 4 3 -1 -1 -2 -1
  0 1 0
  -3 2 1 -2 1 1 1 0 -3 1 -1 0 -1 1 -1 -1 0 1 -1 -1 0 1 3 -1 -3 -2 8 0 -1 0 2 1 1
  -1 2 -4
  -3 -4 2 1 4 -3 1 -2 1 2 1 0 -1 2 2 -1 3 2 0 -1 2 3 -2 -1 -1 4 0 10 4 0 -4 -3 -1
  -2 3 1
  -4 -2 -1 1 -2 -1 2 -3 2 -1 0 -1 0 0 3 0 1 2 -1 0 0 2 1 2 2 3 -1 4 8 -2 -3 -1 2
  0 1 1
  3 0 1 -1 3 -4 -2 2 -2 3 1 0 2 -2 -3 -1 -2 -1 1 -1 2 -1 -2 -3 1 -1 0 0 -2 8 1 -1
  -2 -3 0 -3
  3 0 -1 -1 1 1 -1 3 -2 1 -2 0 -1 -1 -2 1 -2 -3 -2 0 1 -2 1 -1 2 -1 2 -4 -3 1 6 2
  0 0 -2 -1
  3 4 -5 1 0 0 -2 -1 -3 -1 -5 -1 -3 -3 -2 1 -3 1 -1 4 -1 2 3 0 1 -2 1 -3 -1 -1 2
  8 2 4 -2 -3
  -2 0 -3 -2 -1 0 2 -1 -1 1 -2 -1 -1 -1 2 2 0 2 -2 2 1 2 2 -2 2 -1 1 -1 2 -2 0 2
  8 1 1 0
  3 1 -4 3 0 0 0 -1 0 -3 -2 0 -2 -4 -1 0 -2 0 -1 2 -1 1 2 1 3 0 -1 -2 0 -3 0 4 1
  8 -3 -1
  -5 3 4 -2 0 1 -2 -4 1 5 1 3 1 3 0 3 4 3 3 -1 -1 3 0 2 -6 1 2 3 1 0 -2 -2 1 -3
  10 0
  0 -4 3 2 -1 0 0 -1 1 2 1 2 -1 2 3 -1 3 -1 0 0 0 0 -2 -1 1 0 -4 1 1 -3 -1 -3 0
  -1 0 10
  

• MINIMUM
  6
  

• KISSING_NUMBER
  4320
  

• 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