The Lattice A15
An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, RWTH Aachen University
(nebe@math.rwthaachen.de)
and
Neil J. A. Sloane
(njasloane@gmail.com)
Last modified Fri Jul 18 13:09:18 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
A15

DIMENSION
15

DET
16

DIVISORS
1 1 1 1 1 1 1 1 1 1 1 1 1 1 16

MINIMAL_NORM
2

KISSING_NUMBER
240

GROUP_ORDER
41845579776000

GROUP_NAME
C2 x S16 = C2 x W(A15)

GROUP_GENERATORS
2
15
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 1 1
0 0 0 0 0 0 0 0 0 0 0 0 1 1 0
0 0 0 0 0 0 0 0 0 0 0 1 0 1 0
0 0 0 0 0 0 0 0 0 0 1 0 0 1 0
0 0 0 0 0 0 0 0 0 1 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 1 0 0 0 0 0 1 0
0 0 0 0 0 0 1 0 0 0 0 0 0 1 0
0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 0 1 0
0 0 1 0 0 0 0 0 0 0 0 0 0 1 0
0 1 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 0 0 0 0 0 0 0 0 0 0 1 0
15
1 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 1 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 0
0 0 0 0 0 0 0 0 0 0 0 1 0 1 0
0 0 0 0 0 0 0 0 0 0 1 0 0 1 0
0 0 0 0 0 0 0 0 0 1 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 1 0 0 0 0 0 1 0
0 0 0 0 0 0 1 0 0 0 0 0 0 1 0
0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 0 1 0
0 0 1 0 0 0 0 0 0 0 0 0 0 1 0
0 1 0 0 0 0 0 0 0 0 0 0 0 1 0

BASIS
15 16
.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
.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
.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 .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 .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
.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 .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 .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
.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 .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 .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
.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 .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 .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
.000000000000E+00 .000000000000E+00 .100000000000E+01
.100000000000E+01

GLUE_VECTORS
16
.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 .000000000000E+00
.000000000000E+00
.625000000000E01 .625000000000E01 .625000000000E01
.625000000000E01 .625000000000E01 .625000000000E01
.625000000000E01 .625000000000E01 .625000000000E01
.625000000000E01 .625000000000E01 .625000000000E01
.625000000000E01 .625000000000E01 .625000000000E01
.937500000000E+00
.125000000000E+00 .125000000000E+00 .125000000000E+00
.125000000000E+00 .125000000000E+00 .125000000000E+00
.125000000000E+00 .125000000000E+00 .125000000000E+00
.125000000000E+00 .125000000000E+00 .125000000000E+00
.125000000000E+00 .125000000000E+00 .875000000000E+00
.875000000000E+00
.187500000000E+00 .187500000000E+00 .187500000000E+00
.187500000000E+00 .187500000000E+00 .187500000000E+00
.187500000000E+00 .187500000000E+00 .187500000000E+00
.187500000000E+00 .187500000000E+00 .187500000000E+00
.187500000000E+00 .812500000000E+00 .812500000000E+00
.812500000000E+00
.250000000000E+00 .250000000000E+00 .250000000000E+00
.250000000000E+00 .250000000000E+00 .250000000000E+00
.250000000000E+00 .250000000000E+00 .250000000000E+00
.250000000000E+00 .250000000000E+00 .250000000000E+00
.750000000000E+00 .750000000000E+00 .750000000000E+00
.750000000000E+00
.312500000000E+00 .312500000000E+00 .312500000000E+00
.312500000000E+00 .312500000000E+00 .312500000000E+00
.312500000000E+00 .312500000000E+00 .312500000000E+00
.312500000000E+00 .312500000000E+00 .687500000000E+00
.687500000000E+00 .687500000000E+00 .687500000000E+00
.687500000000E+00
.375000000000E+00 .375000000000E+00 .375000000000E+00
.375000000000E+00 .375000000000E+00 .375000000000E+00
.375000000000E+00 .375000000000E+00 .375000000000E+00
.375000000000E+00 .625000000000E+00 .625000000000E+00
.625000000000E+00 .625000000000E+00 .625000000000E+00
.625000000000E+00
.437500000000E+00 .437500000000E+00 .437500000000E+00
.437500000000E+00 .437500000000E+00 .437500000000E+00
.437500000000E+00 .437500000000E+00 .437500000000E+00
.562500000000E+00 .562500000000E+00 .562500000000E+00
.562500000000E+00 .562500000000E+00 .562500000000E+00
.562500000000E+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 .500000000000E+00
.500000000000E+00
.562500000000E+00 .562500000000E+00 .562500000000E+00
.562500000000E+00 .562500000000E+00 .562500000000E+00
.562500000000E+00 .437500000000E+00 .437500000000E+00
.437500000000E+00 .437500000000E+00 .437500000000E+00
.437500000000E+00 .437500000000E+00 .437500000000E+00
.437500000000E+00
.625000000000E+00 .625000000000E+00 .625000000000E+00
.625000000000E+00 .625000000000E+00 .625000000000E+00
.375000000000E+00 .375000000000E+00 .375000000000E+00
.375000000000E+00 .375000000000E+00 .375000000000E+00
.375000000000E+00 .375000000000E+00 .375000000000E+00
.375000000000E+00
.687500000000E+00 .687500000000E+00 .687500000000E+00
.687500000000E+00 .687500000000E+00 .312500000000E+00
.312500000000E+00 .312500000000E+00 .312500000000E+00
.312500000000E+00 .312500000000E+00 .312500000000E+00
.312500000000E+00 .312500000000E+00 .312500000000E+00
.312500000000E+00
.750000000000E+00 .750000000000E+00 .750000000000E+00
.750000000000E+00 .250000000000E+00 .250000000000E+00
.250000000000E+00 .250000000000E+00 .250000000000E+00
.250000000000E+00 .250000000000E+00 .250000000000E+00
.250000000000E+00 .250000000000E+00 .250000000000E+00
.250000000000E+00
.812500000000E+00 .812500000000E+00 .812500000000E+00
.187500000000E+00 .187500000000E+00 .187500000000E+00
.187500000000E+00 .187500000000E+00 .187500000000E+00
.187500000000E+00 .187500000000E+00 .187500000000E+00
.187500000000E+00 .187500000000E+00 .187500000000E+00
.187500000000E+00
.875000000000E+00 .875000000000E+00 .125000000000E+00
.125000000000E+00 .125000000000E+00 .125000000000E+00
.125000000000E+00 .125000000000E+00 .125000000000E+00
.125000000000E+00 .125000000000E+00 .125000000000E+00
.125000000000E+00 .125000000000E+00 .125000000000E+00
.125000000000E+00
.937500000000E+00 .625000000000E01 .625000000000E01
.625000000000E01 .625000000000E01 .625000000000E01
.625000000000E01 .625000000000E01 .625000000000E01
.625000000000E01 .625000000000E01 .625000000000E01
.625000000000E01 .625000000000E01 .625000000000E01
.625000000000E01

TRIANGULAR_BASIS
15 15
.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 .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 .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
.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 .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 .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
.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 .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 .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
.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 .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 .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
.000000000000E+00 .000000000000E+00 .960768922831E+00
.103774904333E+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 .000000000000E+00
.963624111659E+00 .103509833901E+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
.000000000000E+00 .966091783079E+00 .103279555899E+01

GRAM
15 15
2 1 0 0 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 0
0 1 2 1 0 0 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 0 0 1 2 1 0 0 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 0 0 1 2 1 0 0 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 0 0 1 2 1 0 0 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 0 0 1 2 1 0 0 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 0 0 1 2 1 0
0 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 0 0 1 2

PROPERTIES
INTEGRAL =1

LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe