The Lattice D3

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 Sun Dec 16 17:04:17 EST 2001

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
MINIMAL_NORM
KISSING_NUMBER
DENSITY
GROUP_ORDER
HERMITE_NUMBER
BASIS
GLUE_VECTORS
MINVECS
TRIANGULAR_BASIS
GRAM
PROPERTIES
THETA_SERIES
GENUS
COMMENTS
LAST_LINE

• NAME
  D3
  
• DIMENSION
  3
  
• DET
  .400000000000E+01
  
• MINIMAL_NORM
  .200000000000E+01
  
• KISSING_NUMBER
  12
  
• DENSITY
  .176776695297E+00
  
• GROUP_ORDER
  48
  
• HERMITE_NUMBER
  .125992104989E+01
  
• BASIS
  3 3
  .100000000000E+01 .100000000000E+01 .000000000000E+00
  .100000000000E+01 -.100000000000E+01 .000000000000E+00
  .000000000000E+00 .100000000000E+01 -.100000000000E+01
  
• GLUE_VECTORS
  4
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .500000000000E+00 .500000000000E+00 .500000000000E+00
  .000000000000E+00 .000000000000E+00 .100000000000E+01
  .500000000000E+00 .500000000000E+00 -.500000000000E+00
  
• MINVECS
  12 12.00000000
  .000000000000E+00 .100000000000E+01 -.100000000000E+01
  .000000000000E+00 -.100000000000E+01 .100000000000E+01
  .100000000000E+01 -.100000000000E+01 .000000000000E+00
  -.100000000000E+01 .100000000000E+01 .000000000000E+00
  .100000000000E+01 .000000000000E+00 -.100000000000E+01
  -.100000000000E+01 .000000000000E+00 .100000000000E+01
  .000000000000E+00 .100000000000E+01 .100000000000E+01
  .000000000000E+00 -.100000000000E+01 -.100000000000E+01
  .100000000000E+01 .000000000000E+00 .100000000000E+01
  -.100000000000E+01 .000000000000E+00 -.100000000000E+01
  .100000000000E+01 .100000000000E+01 .000000000000E+00
  -.100000000000E+01 -.100000000000E+01 .000000000000E+00
  
• TRIANGULAR_BASIS
  3 3
  .200000000000E+01 .000000000000E+00 .000000000000E+00
  .100000000000E+01 -.100000000000E+01 .000000000000E+00
  .000000000000E+00 .100000000000E+01 -.100000000000E+01
  
• GRAM
  3 3
  2 0 1
  0 2 -1
  1 -1 2
  
• PROPERTIES
  INTEGRAL =1
  
• THETA_SERIES
  0 1
  2 12
  4 6
  6 24
  8 12
  10 24
  
• GENUS
  [2, 1, 4]
  [0, 2, 1]
  [0, 2, 1]
  [0, - 1, - 1]
  [0, 0, 3]
  
• COMMENTS
  This is the face-centered cubic (or f.c.c.) lattice.
  
• LAST_LINE
  

INDEX FILE | ABBREVIATIONS