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 Fri Jul 18 13:09:12 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

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

• NAME
  A12
  

• DIMENSION
  12
  

• DET
  13
  

• DIVISORS
  1 1 1 1 1 1 1 1 1 1 1 13
  

• MINIMAL_NORM
  2
  

• KISSING_NUMBER
  156
  

• GROUP_ORDER
  12454041600
  

• GROUP_NAME
  C2 x S13 = C2 x W(A12)
  

• GROUP_GENERATORS
  2
  12
  0 0 0 0 0 0 0 0 0 0 0 1
  0 0 0 0 0 0 0 0 0 0 -1 1
  0 0 0 0 0 0 0 0 0 -1 0 1
  0 0 0 0 0 0 0 0 -1 0 0 1
  0 0 0 0 0 0 0 -1 0 0 0 1
  0 0 0 0 0 0 -1 0 0 0 0 1
  0 0 0 0 0 -1 0 0 0 0 0 1
  0 0 0 0 -1 0 0 0 0 0 0 1
  0 0 0 -1 0 0 0 0 0 0 0 1
  0 0 -1 0 0 0 0 0 0 0 0 1
  0 -1 0 0 0 0 0 0 0 0 0 1
  -1 0 0 0 0 0 0 0 0 0 0 1
  12
  -1 0 0 0 0 0 0 0 0 0 1 0
  0 0 0 0 0 0 0 0 0 0 1 -1
  0 0 0 0 0 0 0 0 0 0 1 0
  0 0 0 0 0 0 0 0 0 -1 1 0
  0 0 0 0 0 0 0 0 -1 0 1 0
  0 0 0 0 0 0 0 -1 0 0 1 0
  0 0 0 0 0 0 -1 0 0 0 1 0
  0 0 0 0 0 -1 0 0 0 0 1 0
  0 0 0 0 -1 0 0 0 0 0 1 0
  0 0 0 -1 0 0 0 0 0 0 1 0
  0 0 -1 0 0 0 0 0 0 0 1 0
  0 -1 0 0 0 0 0 0 0 0 1 0
  

• BASIS
  12 13
  .100000000000E+01 -.100000000000E+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 .100000000000E+01 -.100000000000E+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 .100000000000E+01
  -.100000000000E+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
  .100000000000E+01 -.100000000000E+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 .100000000000E+01 -.100000000000E+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 .100000000000E+01
  -.100000000000E+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
  .100000000000E+01 -.100000000000E+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 .100000000000E+01 -.100000000000E+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 .100000000000E+01
  -.100000000000E+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
  .100000000000E+01 -.100000000000E+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 .100000000000E+01 -.100000000000E+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 .100000000000E+01
  -.100000000000E+01
  

• GLUE_VECTORS
  13
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  .769230769231E-01 .769230769231E-01 .769230769231E-01
  .769230769231E-01 .769230769231E-01 .769230769231E-01
  .769230769231E-01 .769230769231E-01 .769230769231E-01
  .769230769231E-01 .769230769231E-01 .769230769231E-01
  -.923076923077E+00
  .153846153846E+00 .153846153846E+00 .153846153846E+00
  .153846153846E+00 .153846153846E+00 .153846153846E+00
  .153846153846E+00 .153846153846E+00 .153846153846E+00
  .153846153846E+00 .153846153846E+00 -.846153846154E+00
  -.846153846154E+00
  .230769230769E+00 .230769230769E+00 .230769230769E+00
  .230769230769E+00 .230769230769E+00 .230769230769E+00
  .230769230769E+00 .230769230769E+00 .230769230769E+00
  .230769230769E+00 -.769230769231E+00 -.769230769231E+00
  -.769230769231E+00
  .307692307692E+00 .307692307692E+00 .307692307692E+00
  .307692307692E+00 .307692307692E+00 .307692307692E+00
  .307692307692E+00 .307692307692E+00 .307692307692E+00
  -.692307692308E+00 -.692307692308E+00 -.692307692308E+00
  -.692307692308E+00
  .384615384615E+00 .384615384615E+00 .384615384615E+00
  .384615384615E+00 .384615384615E+00 .384615384615E+00
  .384615384615E+00 .384615384615E+00 -.615384615385E+00
  -.615384615385E+00 -.615384615385E+00 -.615384615385E+00
  -.615384615385E+00
  .461538461538E+00 .461538461538E+00 .461538461538E+00
  .461538461538E+00 .461538461538E+00 .461538461538E+00
  .461538461538E+00 -.538461538462E+00 -.538461538462E+00
  -.538461538462E+00 -.538461538462E+00 -.538461538462E+00
  -.538461538462E+00
  .538461538462E+00 .538461538462E+00 .538461538462E+00
  .538461538462E+00 .538461538462E+00 .538461538462E+00
  -.461538461538E+00 -.461538461538E+00 -.461538461538E+00
  -.461538461538E+00 -.461538461538E+00 -.461538461538E+00
  -.461538461538E+00
  .615384615385E+00 .615384615385E+00 .615384615385E+00
  .615384615385E+00 .615384615385E+00 -.384615384615E+00
  -.384615384615E+00 -.384615384615E+00 -.384615384615E+00
  -.384615384615E+00 -.384615384615E+00 -.384615384615E+00
  -.384615384615E+00
  .692307692308E+00 .692307692308E+00 .692307692308E+00
  .692307692308E+00 -.307692307692E+00 -.307692307692E+00
  -.307692307692E+00 -.307692307692E+00 -.307692307692E+00
  -.307692307692E+00 -.307692307692E+00 -.307692307692E+00
  -.307692307692E+00
  .769230769231E+00 .769230769231E+00 .769230769231E+00
  -.230769230769E+00 -.230769230769E+00 -.230769230769E+00
  -.230769230769E+00 -.230769230769E+00 -.230769230769E+00
  -.230769230769E+00 -.230769230769E+00 -.230769230769E+00
  -.230769230769E+00
  .846153846154E+00 .846153846154E+00 -.153846153846E+00
  -.153846153846E+00 -.153846153846E+00 -.153846153846E+00
  -.153846153846E+00 -.153846153846E+00 -.153846153846E+00
  -.153846153846E+00 -.153846153846E+00 -.153846153846E+00
  -.153846153846E+00
  .923076923077E+00 -.769230769231E-01 -.769230769231E-01
  -.769230769231E-01 -.769230769231E-01 -.769230769231E-01
  -.769230769231E-01 -.769230769231E-01 -.769230769231E-01
  -.769230769231E-01 -.769230769231E-01 -.769230769231E-01
  -.769230769231E-01
  

• TRIANGULAR_BASIS
  12 12
  .141421356237E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  -.707106781187E+00 .122474487139E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 -.816496580928E+00 .115470053838E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 -.866025403784E+00
  .111803398875E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  -.894427191000E+00 .109544511501E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 -.912870929175E+00 .108012344973E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 -.925820099773E+00
  .106904496765E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  -.935414346693E+00 .106066017178E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 -.942809041582E+00 .105409255339E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 -.948683298051E+00
  .104880884817E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  -.953462589246E+00 .104446593573E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 -.957427107756E+00 .104083299973E+01
  

• GRAM
  12 12
  2 -1 0 0 0 0 0 0 0 0 0 0
  -1 2 -1 0 0 0 0 0 0 0 0 0
  0 -1 2 -1 0 0 0 0 0 0 0 0
  0 0 -1 2 -1 0 0 0 0 0 0 0
  0 0 0 -1 2 -1 0 0 0 0 0 0
  0 0 0 0 -1 2 -1 0 0 0 0 0
  0 0 0 0 0 -1 2 -1 0 0 0 0
  0 0 0 0 0 0 -1 2 -1 0 0 0
  0 0 0 0 0 0 0 -1 2 -1 0 0
  0 0 0 0 0 0 0 0 -1 2 -1 0
  0 0 0 0 0 0 0 0 0 -1 2 -1
  0 0 0 0 0 0 0 0 0 0 -1 2
  

• PROPERTIES
  INTEGRAL =1
  

• LAST_LINE
  

  ---

  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe