The Lattice O(5)

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

Last modified Thu Jun 28 23:56:07 EDT 2001

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
MINIMAL_NORM
DET
KISSING_NUMBER
GRAM
GROUP_ORDER
GROUP_GENERATORS
PROPERTIES
NOTES
REFERENCES
LAST_LINE

• NAME
  O(5)
  
• DIMENSION
  8
  
• MINIMAL_NORM
  3
  
• DET
  625
  
• KISSING_NUMBER
  16
  
• GRAM
  8 0
  3
  0 3
  0 0 3
  0 0 0 3
  -1 1 1 1 3
  1 -1 1 1 0 3
  1 1 -1 1 0 0 3
  1 1 1 -1 0 0 0 3
  
• GROUP_ORDER
  384
  
• GROUP_GENERATORS
  4
  8 8
  -1 0 0 0 0 0 0 0
  0 0 1 0 0 0 0 0
  0 -1 0 0 0 0 0 0
  0 0 0 1 0 0 0 0
  0 0 0 0 0 1 0 0
  0 0 0 0 0 0 0 -1
  0 0 0 0 1 0 0 0
  0 0 0 0 0 0 -1 0
  8 8
  0 0 0 0 0 1 0 0
  0 0 0 0 1 0 0 0
  0 0 0 0 0 0 0 -1
  0 0 0 0 0 0 -1 0
  -1 0 0 0 0 0 0 0
  0 -1 0 0 0 0 0 0
  0 0 1 0 0 0 0 0
  0 0 0 1 0 0 0 0
  8 8
  1 0 0 0 0 0 0 0
  0 0 -1 0 0 0 0 0
  0 -1 0 0 0 0 0 0
  0 0 0 1 0 0 0 0
  0 0 0 0 0 0 0 -1
  0 0 0 0 0 1 0 0
  0 0 0 0 0 0 1 0
  0 0 0 0 -1 0 0 0
  8 8
  1 0 0 0 0 0 0 0
  0 0 0 -1 0 0 0 0
  0 -1 0 0 0 0 0 0
  0 0 1 0 0 0 0 0
  0 0 0 0 0 0 -1 0
  0 0 0 0 0 1 0 0
  0 0 0 0 0 0 0 1
  0 0 0 0 -1 0 0 0
  
• PROPERTIES
  INTEGRAL=1
  MODULAR=5
  
• NOTES
  The "odd" version of Q_8(1).
  Construction: Take vector v of norm 8 in L/2L, where L = Q_8(1) = H4.std
  is the Icosian lattice; then this is nbr of Q_8(1) with respect to v.
  
• REFERENCES
  E. M. Rains and N. J. A. Sloane,
  The Shadow Theory of Modular and Unimodular Lattices,
  J. Number Theory, 73 (1998), pp. 359-389;
  http://www.research.att.com/~njas/doc/shad.pdf or shad.ps
  
• LAST_LINE
  

INDEX FILE | ABBREVIATIONS

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