The Lattice A2

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 Sat Oct 2 13:57:40 EDT 1999

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
MINIMAL_NORM
KISSING_NUMBER
GROUP_ORDER
BASIS
GLUE_VECTORS
MINVECS
TRIANGULAR_BASIS
GRAM
PROPERTIES
DIVISORS
GROUP_NAME
GROUP_GENERATORS
NOTES
SEQUENCES
LAST_LINE

• NAME
  A2
  
• DIMENSION
  2
  
• DET
  3
  
• MINIMAL_NORM
  2
  
• KISSING_NUMBER
  6
  
• GROUP_ORDER
  12
  
• BASIS
  2 3
  1 -1 0
  0 1 -1
  
• GLUE_VECTORS
  3
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .333333333333E+00 .333333333333E+00 -.666666666667E+00
  .666666666667E+00 -.333333333333E+00 -.333333333333E+00
  
• MINVECS
  4 6.00000000
  -.707107000000E+00 .122474500000E+01 .707107000000E+00
  -.122474500000E+01 .141421400000E+01 .000000000000E+00
  -.141421400000E+01 .000000000000E+00 .707107000000E+00
  .122474500000E+01 -.707107000000E+00 -.122474500000E+01
  
• TRIANGULAR_BASIS
  2 2
  .141421356237E+01 .000000000000E+00
  -.707106781187E+00 .122474487139E+01
  
• GRAM
  2 2
  2 -1
  -1 2
  
• PROPERTIES
  INTEGRAL =1
  
• DIVISORS
  1 3
  
• GROUP_NAME
  C2 x S3 = C2 x W(A2) = D12
  
• GROUP_GENERATORS
  2
  2
  0 -1
  1 1
  2
  0 1
  1 0
  
• NOTES
  Usually called the hexagonal lattice (see SPLAG); sometimes called
  the triangular lattice.
  
• SEQUENCES
  Theta series
  Shells
  Coordination sequence
  Numbers represented
  Walks on
  Sublattices
  
• LAST_LINE
  

INDEX FILE | ABBREVIATIONS

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