The Lattice A13
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 13:09:14 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
A13
-
DIMENSION
13
-
DET
14
-
DIVISORS
1 14 14 14 14 14 14 14 14 14 14 14 14
-
MINIMAL_NORM
13
-
KISSING_NUMBER
28
-
GROUP_ORDER
174356582400
-
GROUP_NAME
C2 x S14 = C2 x W(A13)
-
GROUP_GENERATORS
2
13
0 -1 0 0 0 0 0 0 0 0 0 0 0
0 0 -1 0 0 0 0 0 0 0 0 0 0
0 0 0 -1 0 0 0 0 0 0 0 0 0
0 0 0 0 -1 0 0 0 0 0 0 0 0
0 0 0 0 0 -1 0 0 0 0 0 0 0
0 0 0 0 0 0 -1 0 0 0 0 0 0
0 0 0 0 0 0 0 -1 0 0 0 0 0
0 0 0 0 0 0 0 0 -1 0 0 0 0
0 0 0 0 0 0 0 0 0 -1 0 0 0
0 0 0 0 0 0 0 0 0 0 -1 0 0
0 0 0 0 0 0 0 0 0 0 0 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 -1
1 1 1 1 1 1 1 1 1 1 1 1 1
13
1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 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 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 0 0 0 0 0 1 0 0 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 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 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0
-
BASIS
13 14
.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
.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 .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 .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
.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 .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 .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
.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 .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 .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
.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 .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 .000000000000E+00
.100000000000E+01 -.100000000000E+01
-
GLUE_VECTORS
14
.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 .000000000000E+00
.714285714286E-01 .714285714286E-01 .714285714286E-01
.714285714286E-01 .714285714286E-01 .714285714286E-01
.714285714286E-01 .714285714286E-01 .714285714286E-01
.714285714286E-01 .714285714286E-01 .714285714286E-01
.714285714286E-01 -.928571428571E+00
.142857142857E+00 .142857142857E+00 .142857142857E+00
.142857142857E+00 .142857142857E+00 .142857142857E+00
.142857142857E+00 .142857142857E+00 .142857142857E+00
.142857142857E+00 .142857142857E+00 .142857142857E+00
-.857142857143E+00 -.857142857143E+00
.214285714286E+00 .214285714286E+00 .214285714286E+00
.214285714286E+00 .214285714286E+00 .214285714286E+00
.214285714286E+00 .214285714286E+00 .214285714286E+00
.214285714286E+00 .214285714286E+00 -.785714285714E+00
-.785714285714E+00 -.785714285714E+00
.285714285714E+00 .285714285714E+00 .285714285714E+00
.285714285714E+00 .285714285714E+00 .285714285714E+00
.285714285714E+00 .285714285714E+00 .285714285714E+00
.285714285714E+00 -.714285714286E+00 -.714285714286E+00
-.714285714286E+00 -.714285714286E+00
.357142857143E+00 .357142857143E+00 .357142857143E+00
.357142857143E+00 .357142857143E+00 .357142857143E+00
.357142857143E+00 .357142857143E+00 .357142857143E+00
-.642857142857E+00 -.642857142857E+00 -.642857142857E+00
-.642857142857E+00 -.642857142857E+00
.428571428571E+00 .428571428571E+00 .428571428571E+00
.428571428571E+00 .428571428571E+00 .428571428571E+00
.428571428571E+00 .428571428571E+00 -.571428571429E+00
-.571428571429E+00 -.571428571429E+00 -.571428571429E+00
-.571428571429E+00 -.571428571429E+00
.500000000000E+00 .500000000000E+00 .500000000000E+00
.500000000000E+00 .500000000000E+00 .500000000000E+00
.500000000000E+00 -.500000000000E+00 -.500000000000E+00
-.500000000000E+00 -.500000000000E+00 -.500000000000E+00
-.500000000000E+00 -.500000000000E+00
.571428571429E+00 .571428571429E+00 .571428571429E+00
.571428571429E+00 .571428571429E+00 .571428571429E+00
-.428571428571E+00 -.428571428571E+00 -.428571428571E+00
-.428571428571E+00 -.428571428571E+00 -.428571428571E+00
-.428571428571E+00 -.428571428571E+00
.642857142857E+00 .642857142857E+00 .642857142857E+00
.642857142857E+00 .642857142857E+00 -.357142857143E+00
-.357142857143E+00 -.357142857143E+00 -.357142857143E+00
-.357142857143E+00 -.357142857143E+00 -.357142857143E+00
-.357142857143E+00 -.357142857143E+00
.714285714286E+00 .714285714286E+00 .714285714286E+00
.714285714286E+00 -.285714285714E+00 -.285714285714E+00
-.285714285714E+00 -.285714285714E+00 -.285714285714E+00
-.285714285714E+00 -.285714285714E+00 -.285714285714E+00
-.285714285714E+00 -.285714285714E+00
.785714285714E+00 .785714285714E+00 .785714285714E+00
-.214285714286E+00 -.214285714286E+00 -.214285714286E+00
-.214285714286E+00 -.214285714286E+00 -.214285714286E+00
-.214285714286E+00 -.214285714286E+00 -.214285714286E+00
-.214285714286E+00 -.214285714286E+00
.857142857143E+00 .857142857143E+00 -.142857142857E+00
-.142857142857E+00 -.142857142857E+00 -.142857142857E+00
-.142857142857E+00 -.142857142857E+00 -.142857142857E+00
-.142857142857E+00 -.142857142857E+00 -.142857142857E+00
-.142857142857E+00 -.142857142857E+00
.928571428571E+00 -.714285714286E-01 -.714285714286E-01
-.714285714286E-01 -.714285714286E-01 -.714285714286E-01
-.714285714286E-01 -.714285714286E-01 -.714285714286E-01
-.714285714286E-01 -.714285714286E-01 -.714285714286E-01
-.714285714286E-01 -.714285714286E-01
-
TRIANGULAR_BASIS
13 13
.141421356237E+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
-.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
.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 .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 .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
.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 .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 .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
.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 .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 .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
.000000000000E+00 -.957427107756E+00 .104083299973E+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 -.960768922831E+00
.103774904333E+01
-
GRAM
13 13
2 -1 0 0 0 0 0 0 0 0 0 0 0
-1 2 -1 0 0 0 0 0 0 0 0 0 0
0 -1 2 -1 0 0 0 0 0 0 0 0 0
0 0 -1 2 -1 0 0 0 0 0 0 0 0
0 0 0 -1 2 -1 0 0 0 0 0 0 0
0 0 0 0 -1 2 -1 0 0 0 0 0 0
0 0 0 0 0 -1 2 -1 0 0 0 0 0
0 0 0 0 0 0 -1 2 -1 0 0 0 0
0 0 0 0 0 0 0 -1 2 -1 0 0 0
0 0 0 0 0 0 0 0 -1 2 -1 0 0
0 0 0 0 0 0 0 0 0 -1 2 -1 0
0 0 0 0 0 0 0 0 0 0 -1 2 -1
0 0 0 0 0 0 0 0 0 0 0 -1 2
-
PROPERTIES
INTEGRAL =1
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe