The Lattice mcc
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 13:19:34 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
MINIMAL_NORM
DENSITY
GROUP_ORDER
TRIANGULAR_BASIS
GRAM
GRAM(MAPLE)
GRAM(PARI)
PROPERTIES
NOTES
REFERENCES
EIGENVALUES
THETA_SERIES
LAST_LINE
-
NAME
mcc
-
DIMENSION
3
-
DET
1
-
MINIMAL_NORM
1.20710678118654752440
-
DENSITY
.165778630469E+00
-
GROUP_ORDER
16
-
TRIANGULAR_BASIS
3 3
.109868411347E+01 .000000000000E+00 .000000000000E+00
-.455089860701E+00 .999999999939E+00 .000000000000E+00
-.188504392394E+00 -.585786437865E+00 .910179720963E+00
-
GRAM
3 3
.120710678119E+01 -.500000000153E+00 -.207106781242E+00
-.500000000153E+00 .120710678119E+01 -.500000000153E+00
-.207106781242E+00 -.500000000153E+00 .120710678119E+01
-
GRAM(MAPLE)
s2:=sqrt(2); linalg[ matrix](
[ [ 1+s2,-1,-1],[ -1,1+s2,1-s2],[ -1,1-s2,1+s2]])/2;
-
GRAM(PARI)
s2=sqrt(2)
[ 1+s2,-1,-1; -1,1+s2,1-s2; -1,1-s2,1+s2]/2
-
PROPERTIES
INTEGRAL =0
-
NOTES
The "mean-centered cuboidal" lattice, the densest iso-dual lattice
in 3 dimensions.
-
REFERENCES
1. J. H. Conway and N. J. A. Sloane,
On Lattices Equivalent to Their Duals,
J. Number Theory, Vol. 48, 1994, pp. 373-382.
M. Bernstein and N. J. A. Sloane,
Some Lattices Obtained from Riemann Surfaces,
in "Extremal Riemann Surfaces" (Contemporary Math. Vol. 201),
J. R. Quine and P. Sarnak (editors),
Amer. Math. Soc., Providence, RI, 1997, pp. 29-32.
-
EIGENVALUES
.120710678119E+01 .999999999877E+00 .828427124452E+00
-
THETA_SERIES
0.000000D+00 1
0.120711D+01 8
0.141421D+01 4
0.200000D+01 2
0.282843D+01 4
0.341421D+01 8
0.403553D+01 16
0.482843D+01 8
0.520711D+01 8
0.565685D+01 4
0.686396D+01 8
0.707107D+01 8
0.765685D+01 8
0.800000D+01 2
0.803553D+01 16
0.907107D+01 16
0.941421D+01 8
0.969239D+01 16
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe