The Lattice D3
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 13:13:19 CEST 2014
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
Haftungsausschluss/Disclaimer
Gabriele Nebe