The Lattice K12 (The Coxeter-Todd Lattice)
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 13:16:45 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
MINIMAL_NORM
KISSING_NUMBER
DENSITY
HERMITE_NUMBER
PROPERTIES
REFERENCES
GRAM
AUTO
SIMILARITY
BASIS (for a different version but on the same scale)
LAST_LINE
-
NAME
K12 (The Coxeter-Todd Lattice)
-
DIMENSION
12
-
DET
729
-
MINIMAL_NORM
4
-
KISSING_NUMBER
756
-
DENSITY
.370370370370E-01
-
HERMITE_NUMBER
.230940107676E+01
-
PROPERTIES
INTEGRAL=1
MODULAR=3
-
REFERENCES
For the long history of this lattice, and many constructions, see
J. H. Conway and N. J. A. Sloane,
The Coxeter-Todd Lattice, The Mitchell Group and Related Sphere Packings,
Math. Proc. Comb. Phil. Soc. volume 93 1983 pages 421-440.
Also SPLAG 127.
-
GRAM
12 0
4
0 4
0 0 4
-2 0 0 4
0 -2 0 0 4
0 0 -2 0 0 4
2 2 2 -1 -1 -1 4
-1 -1 2 -1 2 -1 0 4
-1 -1 2 2 -1 -1 0 0 4
-1 -1 -1 2 2 2 -2 0 0 4
2 -1 -1 -1 -1 2 0 -2 0 0 4
-1 2 -1 -1 -1 2 0 0 -2 0 0 4
-
AUTO
12
0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 1 -1 -1 0 1 -1 1 1 0
0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0
1 -1 -1 0 0 0 1 0 1 0 -1 1
0 0 0 0 0 -1 0 0 0 1 1 1
0 0 0 0 -1 0 0 1 -1 1 0 -1
0 0 0 0 -1 -1 0 0 0 1 0 0
0 0 -1 0 0 0 1 1 1 0 0 0
0 -1 0 0 0 0 1 -1 0 0 -1 1
0 -1 -1 0 0 0 1 0 0 0 0 0
12
-2 0 0 0 0 0 1 0 -1 0 1 -1
0 0 0 0 0 0 1 0 0 0 0 0
0 0 2 0 0 0 -1 -1 -1 0 0 0
0 0 0 -2 0 0 0 -1 1 1 -1 0
0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 2 0 0 0 -1 -1 -1
-1 1 1 0 0 0 0 0 -1 0 1 -1
1 0 1 1 0 0 -1 0 -1 0 0 0
0 0 1 -1 0 0 -1 -1 0 0 -1 0
0 0 0 -1 1 1 0 -1 1 0 -1 0
-1 0 0 0 0 1 0 0 0 -1 0 -1
1 0 0 1 0 1 0 1 0 -1 0 0
12
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 -1 0 0 0 1 1 1 0 0 0
0 0 0 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 -1 0 0 0 1 1 1
0 0 0 0 0 0 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 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 1 0
0 0 0 0 0 0 0 0 0 0 0 1
-
SIMILARITY
12
-1 0 0 -2 0 0 0 0 0 0 0 0
0 -1 0 0 -2 0 0 0 0 0 0 0
0 0 -1 0 0 -2 0 0 0 0 0 0
2 0 0 1 0 0 0 0 0 0 0 0
0 2 0 0 1 0 0 0 0 0 0 0
0 0 2 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 -1 0 0 -2 0 0
0 0 0 0 0 0 0 -1 0 0 -2 0
0 0 0 0 0 0 0 0 -1 0 0 -2
0 0 0 0 0 0 2 0 0 1 0 0
0 0 0 0 0 0 0 2 0 0 1 0
0 0 0 0 0 0 0 0 2 0 0 1
-
BASIS (for a different version but on the same scale)
12 12
.200000000000E+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 .200000000000E+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 .200000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
-.100000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.173205080757E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 -.100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .173205080757E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 -.100000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .173205080757E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.100000000000E+01 -.500000000000E+00 -.500000000000E+00
.100000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .866025403784E+00 .866025403784E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
-.500000000000E+00 .100000000000E+01 -.500000000000E+00
.000000000000E+00 .100000000000E+01 .000000000000E+00
.866025403784E+00 .000000000000E+00 .866025403784E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
-.500000000000E+00 -.500000000000E+00 .100000000000E+01
.000000000000E+00 .000000000000E+00 .100000000000E+01
.866025403784E+00 .866025403784E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
-.500000000000E+00 -.500000000000E+00 -.500000000000E+00
-.500000000000E+00 .000000000000E+00 .000000000000E+00
.866025403784E+00 -.866025403784E+00 -.866025403784E+00
.866025403784E+00 .000000000000E+00 .000000000000E+00
-.500000000000E+00 -.500000000000E+00 -.500000000000E+00
.000000000000E+00 -.500000000000E+00 .000000000000E+00
-.866025403784E+00 .866025403784E+00 -.866025403784E+00
.000000000000E+00 .866025403784E+00 .000000000000E+00
-.500000000000E+00 -.500000000000E+00 -.500000000000E+00
.000000000000E+00 .000000000000E+00 -.500000000000E+00
-.866025403784E+00 -.866025403784E+00 .866025403784E+00
.000000000000E+00 .000000000000E+00 .866025403784E+00
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe