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 Wed Feb 15 13:50:11 CET 2012

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
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe