The Lattice A4
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 13:09:53 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
MINIMAL_NORM
KISSING_NUMBER
DENSITY
GROUP_ORDER
BASIS
GLUE_VECTORS
TRIANGULAR_BASIS
GRAM
PROPERTIES
DIVISORS
GROUP_NAME
GROUP_GENERATORS
LAST_LINE
-
NAME
A4
-
DIMENSION
4
-
DET
5
-
MINIMAL_NORM
2
-
KISSING_NUMBER
20
-
DENSITY
.111803398875E+00
-
GROUP_ORDER
240
-
BASIS
4 5
.100000000000E+01 -.100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .100000000000E+01 -.100000000000E+01
.000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .100000000000E+01
-.100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.100000000000E+01 -.100000000000E+01
-
GLUE_VECTORS
5
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.200000000000E+00 .200000000000E+00 .200000000000E+00
.200000000000E+00 -.800000000000E+00
.400000000000E+00 .400000000000E+00 .400000000000E+00
-.600000000000E+00 -.600000000000E+00
.600000000000E+00 .600000000000E+00 -.400000000000E+00
-.400000000000E+00 -.400000000000E+00
.800000000000E+00 -.200000000000E+00 -.200000000000E+00
-.200000000000E+00 -.200000000000E+00
-
TRIANGULAR_BASIS
4 4
.141421356237E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00
-.707106781187E+00 .122474487139E+01 .000000000000E+00
.000000000000E+00
.000000000000E+00 -.816496580928E+00 .115470053838E+01
.000000000000E+00
.000000000000E+00 .000000000000E+00 -.866025403784E+00
.111803398875E+01
-
GRAM
4 4
2 -1 0 0
-1 2 -1 0
0 -1 2 -1
0 0 -1 2
-
PROPERTIES
INTEGRAL =1
-
DIVISORS
1 1 1 5
-
GROUP_NAME
C2 x S5 = C2 x W(A4)
-
GROUP_GENERATORS
2
4
0 0 0 1
-1 0 0 1
0 -1 0 1
0 0 -1 1
4
0 1 0 0
1 0 0 0
0 0 1 0
0 0 0 1
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe