The Lattice A21
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 13:09:36 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
A21

DIMENSION
21

DET
22

DIVISORS
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 22

MINIMAL_NORM
2

KISSING_NUMBER
462

GROUP_ORDER
2248001455555215360000

GROUP_NAME
C2 x S22 = C2 x W(A21)

GROUP_GENERATORS
2
21
0 0 0 0 0 0 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 0 0
0 0 0 0 1 1
0 0 0 0 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 0 0 0
0 0 1 0 1 0
0 0 0 0 0 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 0 0 0 0 0 0
1 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 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 1 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 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 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0
0 0 1 0 0 0 0 0 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 0 0 0
0 0 0 0 1 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0
21
1 0 0 0 0 0 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 0 0
0 0 0 0 1 1
0 0 0 0 0 0 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 0 0
0 0 0 1 1 0
0 0 0 0 0 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 0 0 0 0 0
0 1 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 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 1 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 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 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0
0 0 1 0 0 0 0 0 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 0 0 0
0 0 0 0 1 0

BASIS
21 22
.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 .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
.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
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.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 .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
.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
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.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
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.000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .100000000000E+01
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.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
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.000000000000E+00 .000000000000E+00 .000000000000E+00
.100000000000E+01 .100000000000E+01 .000000000000E+00
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.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
.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 .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
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.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
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.100000000000E+01 .100000000000E+01 .000000000000E+00
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.000000000000E+00 .000000000000E+00 .000000000000E+00
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.000000000000E+00 .100000000000E+01 .100000000000E+01
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.000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
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.000000000000E+00 .000000000000E+00 .100000000000E+01
.100000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
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.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 .000000000000E+00 .000000000000E+00
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.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 .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
.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 .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 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .100000000000E+01
.100000000000E+01

GLUE_VECTORS
22
.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 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.454545454545E01 .454545454545E01 .454545454545E01
.454545454545E01 .454545454545E01 .454545454545E01
.454545454545E01 .454545454545E01 .454545454545E01
.454545454545E01 .454545454545E01 .454545454545E01
.454545454545E01 .454545454545E01 .454545454545E01
.454545454545E01 .454545454545E01 .454545454545E01
.454545454545E01 .454545454545E01 .454545454545E01
.954545454545E+00
.909090909091E01 .909090909091E01 .909090909091E01
.909090909091E01 .909090909091E01 .909090909091E01
.909090909091E01 .909090909091E01 .909090909091E01
.909090909091E01 .909090909091E01 .909090909091E01
.909090909091E01 .909090909091E01 .909090909091E01
.909090909091E01 .909090909091E01 .909090909091E01
.909090909091E01 .909090909091E01 .909090909091E+00
.909090909091E+00
.136363636364E+00 .136363636364E+00 .136363636364E+00
.136363636364E+00 .136363636364E+00 .136363636364E+00
.136363636364E+00 .136363636364E+00 .136363636364E+00
.136363636364E+00 .136363636364E+00 .136363636364E+00
.136363636364E+00 .136363636364E+00 .136363636364E+00
.136363636364E+00 .136363636364E+00 .136363636364E+00
.136363636364E+00 .863636363636E+00 .863636363636E+00
.863636363636E+00
.181818181818E+00 .181818181818E+00 .181818181818E+00
.181818181818E+00 .181818181818E+00 .181818181818E+00
.181818181818E+00 .181818181818E+00 .181818181818E+00
.181818181818E+00 .181818181818E+00 .181818181818E+00
.181818181818E+00 .181818181818E+00 .181818181818E+00
.181818181818E+00 .181818181818E+00 .181818181818E+00
.818181818182E+00 .818181818182E+00 .818181818182E+00
.818181818182E+00
.227272727273E+00 .227272727273E+00 .227272727273E+00
.227272727273E+00 .227272727273E+00 .227272727273E+00
.227272727273E+00 .227272727273E+00 .227272727273E+00
.227272727273E+00 .227272727273E+00 .227272727273E+00
.227272727273E+00 .227272727273E+00 .227272727273E+00
.227272727273E+00 .227272727273E+00 .772727272727E+00
.772727272727E+00 .772727272727E+00 .772727272727E+00
.772727272727E+00
.272727272727E+00 .272727272727E+00 .272727272727E+00
.272727272727E+00 .272727272727E+00 .272727272727E+00
.272727272727E+00 .272727272727E+00 .272727272727E+00
.272727272727E+00 .272727272727E+00 .272727272727E+00
.272727272727E+00 .272727272727E+00 .272727272727E+00
.272727272727E+00 .727272727273E+00 .727272727273E+00
.727272727273E+00 .727272727273E+00 .727272727273E+00
.727272727273E+00
.318181818182E+00 .318181818182E+00 .318181818182E+00
.318181818182E+00 .318181818182E+00 .318181818182E+00
.318181818182E+00 .318181818182E+00 .318181818182E+00
.318181818182E+00 .318181818182E+00 .318181818182E+00
.318181818182E+00 .318181818182E+00 .318181818182E+00
.681818181818E+00 .681818181818E+00 .681818181818E+00
.681818181818E+00 .681818181818E+00 .681818181818E+00
.681818181818E+00
.363636363636E+00 .363636363636E+00 .363636363636E+00
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.363636363636E+00 .363636363636E+00 .363636363636E+00
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.636363636364E+00
.409090909091E+00 .409090909091E+00 .409090909091E+00
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.409090909091E+00 .409090909091E+00 .409090909091E+00
.409090909091E+00 .409090909091E+00 .409090909091E+00
.409090909091E+00 .590909090909E+00 .590909090909E+00
.590909090909E+00 .590909090909E+00 .590909090909E+00
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.590909090909E+00
.454545454545E+00 .454545454545E+00 .454545454545E+00
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.545454545455E+00
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.454545454545E+00
.590909090909E+00 .590909090909E+00 .590909090909E+00
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.409090909091E+00 .409090909091E+00 .409090909091E+00
.409090909091E+00 .409090909091E+00 .409090909091E+00
.409090909091E+00
.636363636364E+00 .636363636364E+00 .636363636364E+00
.636363636364E+00 .636363636364E+00 .636363636364E+00
.636363636364E+00 .636363636364E+00 .363636363636E+00
.363636363636E+00 .363636363636E+00 .363636363636E+00
.363636363636E+00 .363636363636E+00 .363636363636E+00
.363636363636E+00 .363636363636E+00 .363636363636E+00
.363636363636E+00 .363636363636E+00 .363636363636E+00
.363636363636E+00
.681818181818E+00 .681818181818E+00 .681818181818E+00
.681818181818E+00 .681818181818E+00 .681818181818E+00
.681818181818E+00 .318181818182E+00 .318181818182E+00
.318181818182E+00 .318181818182E+00 .318181818182E+00
.318181818182E+00 .318181818182E+00 .318181818182E+00
.318181818182E+00 .318181818182E+00 .318181818182E+00
.318181818182E+00 .318181818182E+00 .318181818182E+00
.318181818182E+00
.727272727273E+00 .727272727273E+00 .727272727273E+00
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.272727272727E+00 .272727272727E+00 .272727272727E+00
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GRAM
21 21
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0 0 0 1 2

PROPERTIES
INTEGRAL =1

LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe