The Lattice K12 (The Coxeter-Todd Lattice)

An entry from the Catalogue of Lattices, which is a joint project of
Neil J. A. Sloane, AT&T Labs-Research (njas@research.att.com) and
Gabriele Nebe, University of Ulm (nebe@mathematik.uni-ulm.de)

Last modified Thu Jan 1 13:34:56 EST 1998

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
MINIMAL_NORM
KISSING_NUMBER
DENSITY
HERMITE_NUMBER
PROPERTIES
REFERENCES
GRAM
AUTO
SIMILARITY
BASIS (for a different version but on the same scale)
LAST_LINE

• NAME
  K12 (The Coxeter-Todd Lattice)
  
• DIMENSION
  12
  
• DET
  729
  
• MINIMAL_NORM
  4
  
• KISSING_NUMBER
  756
  
• DENSITY
  .370370370370E-01
  
• HERMITE_NUMBER
  .230940107676E+01
  
• PROPERTIES
  INTEGRAL=1
  MODULAR=3
  
• REFERENCES
  For the long history of this lattice, and many constructions, see
  J. H. Conway and N. J. A. Sloane,
  The Coxeter-Todd Lattice, The Mitchell Group and Related Sphere Packings,
  Math. Proc. Comb. Phil. Soc. volume 93 1983 pages 421-440.
  Also SPLAG 127.
  
• GRAM
  12 0
  4
  0 4
  0 0 4
  -2 0 0 4
  0 -2 0 0 4
  0 0 -2 0 0 4
  2 2 2 -1 -1 -1 4
  -1 -1 2 -1 2 -1 0 4
  -1 -1 2 2 -1 -1 0 0 4
  -1 -1 -1 2 2 2 -2 0 0 4
  2 -1 -1 -1 -1 2 0 -2 0 0 4
  -1 2 -1 -1 -1 2 0 0 -2 0 0 4
  
• AUTO
  12
  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 0 0 1 -1 -1 0 1 -1 1 1 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
  1 -1 -1 0 0 0 1 0 1 0 -1 1
  0 0 0 0 0 -1 0 0 0 1 1 1
  0 0 0 0 -1 0 0 1 -1 1 0 -1
  0 0 0 0 -1 -1 0 0 0 1 0 0
  0 0 -1 0 0 0 1 1 1 0 0 0
  0 -1 0 0 0 0 1 -1 0 0 -1 1
  0 -1 -1 0 0 0 1 0 0 0 0 0
  12
  -2 0 0 0 0 0 1 0 -1 0 1 -1
  0 0 0 0 0 0 1 0 0 0 0 0
  0 0 2 0 0 0 -1 -1 -1 0 0 0
  0 0 0 -2 0 0 0 -1 1 1 -1 0
  0 0 0 0 0 0 0 0 0 1 0 0
  0 0 0 0 0 2 0 0 0 -1 -1 -1
  -1 1 1 0 0 0 0 0 -1 0 1 -1
  1 0 1 1 0 0 -1 0 -1 0 0 0
  0 0 1 -1 0 0 -1 -1 0 0 -1 0
  0 0 0 -1 1 1 0 -1 1 0 -1 0
  -1 0 0 0 0 1 0 0 0 -1 0 -1
  1 0 0 1 0 1 0 1 0 -1 0 0
  12
  1 0 0 0 0 0 0 0 0 0 0 0
  0 1 0 0 0 0 0 0 0 0 0 0
  0 0 -1 0 0 0 1 1 1 0 0 0
  0 0 0 1 0 0 0 0 0 0 0 0
  0 0 0 0 1 0 0 0 0 0 0 0
  0 0 0 0 0 -1 0 0 0 1 1 1
  0 0 0 0 0 0 1 0 0 0 0 0
  0 0 0 0 0 0 0 1 0 0 0 0
  0 0 0 0 0 0 0 0 1 0 0 0
  0 0 0 0 0 0 0 0 0 1 0 0
  0 0 0 0 0 0 0 0 0 0 1 0
  0 0 0 0 0 0 0 0 0 0 0 1
  
• SIMILARITY
  12
  -1 0 0 -2 0 0 0 0 0 0 0 0
  0 -1 0 0 -2 0 0 0 0 0 0 0
  0 0 -1 0 0 -2 0 0 0 0 0 0
  2 0 0 1 0 0 0 0 0 0 0 0
  0 2 0 0 1 0 0 0 0 0 0 0
  0 0 2 0 0 1 0 0 0 0 0 0
  0 0 0 0 0 0 -1 0 0 -2 0 0
  0 0 0 0 0 0 0 -1 0 0 -2 0
  0 0 0 0 0 0 0 0 -1 0 0 -2
  0 0 0 0 0 0 2 0 0 1 0 0
  0 0 0 0 0 0 0 2 0 0 1 0
  0 0 0 0 0 0 0 0 2 0 0 1
  
• BASIS (for a different version but on the same scale)
  12 12
  .200000000000E+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 .200000000000E+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 .200000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  -.100000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .173205080757E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 -.100000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .173205080757E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 -.100000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .173205080757E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .100000000000E+01 -.500000000000E+00 -.500000000000E+00
  .100000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .866025403784E+00 .866025403784E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  -.500000000000E+00 .100000000000E+01 -.500000000000E+00
  .000000000000E+00 .100000000000E+01 .000000000000E+00
  .866025403784E+00 .000000000000E+00 .866025403784E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  -.500000000000E+00 -.500000000000E+00 .100000000000E+01
  .000000000000E+00 .000000000000E+00 .100000000000E+01
  .866025403784E+00 .866025403784E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  -.500000000000E+00 -.500000000000E+00 -.500000000000E+00
  -.500000000000E+00 .000000000000E+00 .000000000000E+00
  .866025403784E+00 -.866025403784E+00 -.866025403784E+00
  .866025403784E+00 .000000000000E+00 .000000000000E+00
  -.500000000000E+00 -.500000000000E+00 -.500000000000E+00
  .000000000000E+00 -.500000000000E+00 .000000000000E+00
  -.866025403784E+00 .866025403784E+00 -.866025403784E+00
  .000000000000E+00 .866025403784E+00 .000000000000E+00
  -.500000000000E+00 -.500000000000E+00 -.500000000000E+00
  .000000000000E+00 .000000000000E+00 -.500000000000E+00
  -.866025403784E+00 -.866025403784E+00 .866025403784E+00
  .000000000000E+00 .000000000000E+00 .866025403784E+00
  
• LAST_LINE
  

INDEX FILE | ABBREVIATIONS

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