晶格S1^2
格目录中的条目,这是一个联合项目
Gabriele Nebe,亚琛RWTH大学(nebe@math.rwth-aachen.de)和
尼尔·J·A·斯隆(njasloane@gmail.com)
上次修改时间:2014年7月18日星期五13:11:22 CEST
索引文件|缩写
此文件的内容
名称
尺寸
亲吻_编号
克
除数(初等除数)
最小_形式
HERMITE_NUMBER公司
HERMITIAN_集团_订单
HERMITIAN_集团_发电机
HERMITIAN_结构
属性
参考文献
注释
最后一行
-
名称
S1^2号
-
尺寸
32
-
亲吻_编号
1728
-
克
32 32
4 -2 2 2 2 -1 0 0 -1 1 0 0 1 -1 -1 1 2 0 2 0 0 0 0 1 2 2 -1 1 1 -1 -1 0
-2 4 -2 -2 -1 2 -1 -1 1 -1 1 1 -1 0 1 0 -2 0 0 0 0 -1 -1 -1 -2 -2 2 1 -1 -1 1 1
2 -2 4 0 1 -1 1 1 0 0 -1 1 2 -1 0 -1 0 0 2 0 0 -1 1 0 2 2 -1 0 2 0 0 -1
2 -2 0 4 1 -1 -1 -1 -2 2 -1 -1 0 -1 0 1 2 0 0 0 0 1 1 0 0 0 -1 0 0 0 0 -1
2 -1 1 1 4 -2 -1 1 1 2 -1 -1 2 -2 -1 1 0 0 2 0 0 1 1 1 0 0 0 -1 2 -2 0 1
-1 2 -1 -1 -2 4 1 0 0 -2 0 2 -2 1 0 -1 -1 0 0 0 0 0 0 -1 -1 -1 0 2 -1 1 1 -1
0 -1 1 -1 -1 1 4 2 1 -2 -1 1 0 0 -1 -2 1 0 -1 0 0 1 0 1 2 2 -2 1 0 2 -1 0
0 -1 1 -1 1 0 2 4 2 -1 -1 1 1 -1 -2 -1 -1 0 1 0 0 1 0 0 0 0 -2 -1 2 0 -1 1
-1 1 0 -2 1 0 1 2 4 -1 -1 1 1 0 0 0 -2 0 1 0 0 0 -1 0 -1 -1 0 -1 1 -1 -1 1
1 -1 0 2 2 -2 -2 -1 -1 4 -1 -1 0 -1 1 2 1 0 0 0 0 1 1 0 -1 -1 0 -1 1 -1 1 0
0 1 -1 -1 -1 0 -1 -1 -1 -1 4 -1 -1 1 -1 0 0 0 0 0 0 -1 -2 1 1 1 1 1 -1 0 0 1
0 1 1-1-1 2 1 1 1-1 4-1 0 1 0-1 0 1 0 0-1-1-1-2-1 0 1 0 0 0
1 -1 2 0 2 -2 0 1 1 0 -1 -1 4 -1 -1 0 -1 0 2 0 0 -1 1 0 1 1 0 -1 1 -1 -1 0
-1 0 -1 -1 -2 1 0 -1 0 -1 1 0 -1 4 0 1 0 0 -1 0 0 -1 -1 0 0 0 1 0 -2 1 -1 -1
-1 1 0 0 -1 0 -1 -2 0 1 -1 1 -1 0 4 0 0 0 -1 0 0 -1 0 -1 -1 -1 1 0 0 0 1 -1
1 0 -1 1 1 -1 -2 -1 0 2 0 0 0 1 0 4 0 0 1 0 0 0 -1 -1 -1 -1 1 -1 0 -2 -1 1
2 -2 0 2 0 -1 1 -1 -2 1 0 -1 -1 0 0 0 8 2 -4 -2 -2 2 -1 1 0 0 -3 2 -3 2 -2 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 -2 0 -2 1 -1 -1 0 0 -1 -1 -1 2 1 -1
2 0 2 0 2 0 -1 1 1 0 0 1 2 -1 -1 1 -4 -2 8 2 2 -1 0 -1 2 2 0 1 4 -4 -1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 2 4 2 -1 1 -1 2 2 1 -1 1 0 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0-2 2 2 4 0 2-1 2 0 1-1 1-1 0 2
0 -1 -1 1 1 0 1 1 0 1 -1 -1 -1 -1 -1 0 2 1 -1 -1 0 6 0 0 1 0 -3 -1 0 0 0 1
0 -1 1 1 1 0 0 0 -1 1 -2 -1 1 -1 0 -1 -1 -1 0 1 2 0 6 -1 1 0 1 -1 1 0 2 0
1 -1 0 0 1 -1 1 0 0 0 1 -2 0 0 -1 -1 1 -1 -1 -1 -1 0 -1 6 1 2 0 1 0 1 0 -1
2 -2 2 0 0 -1 2 0 -1 -1 1 -1 1 0 -1 -1 0 0 2 2 2 1 1 1 8 6 0 0 2 0 0 2
2 -2 2 0 0 -1 2 0 -1 -1 1 -1 1 0 -1 -1 0 0 2 2 0 0 0 2 6 8 -1 1 1 0 -1 1
-1 2 -1 -1 0 0 -2 -2 0 0 1 0 0 1 1 1 -3 -1 0 1 1 -3 1 0 0 -1 6 -1 0 -1 2 1
1 1 0 0-1 2 1-1-1 1 1-1 0-1 2-1 1-1-1 1 0 1-1 6-1 0-1
1 -1 2 0 2 -1 0 2 1 1 -1 1 1 -2 0 0 -3 -1 4 1 1 0 1 0 2 1 0 -1 6 -2 1 1
-1 -1 0 0 -2 1 2 0 -1 -1 0 0 -1 1 0 -2 2 2 -4 0 -1 0 0 1 0 0 -1 0 -2 6 2 -3
-1 1 0 0 0 1 -1 -1 -1 1 0 0 -1 -1 1 -1 -2 1 -1 1 0 0 2 0 0 -1 2 -1 1 2 6 -1
0 1 -1 -1 1 -1 0 1 1 0 1 0 0 -1 -1 1 -1 -1 1 1 2 1 0 -1 2 1 1 -1 1 -3 -1 6
-
除数(初等除数)
2^16
-
最小_形式
4
-
HERMITE_NUMBER公司
2.83
-
HERMITIAN_集团_订单
2^19*3^7=1146617856
-
HERMITIAN_集团_发电机
5
32 32
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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1 -1 1 0 -2 0 0 0 0 0 1 0 1 0 1 0 -1 1 0 1 -1 2 1 1 -1 -1 1 1 0 0 -1 1
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0 0 1 0 -1 0 -1 1 0 0 -1 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0
1 1-1 0 1-2 2-1-1 0 1 1-1 1-1 0 2 1-3 0 2 1 1-2-1-1-1 1
0 -1 0 0 0 0 3 0 -1 0 1 -1 0 0 1 0 0 2 1 -1 1 0 0 0 -1 0 1 0 0 -1 0 0
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1 0 0 0 -1 -1 1 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 -1 0 1 0 0 0 0 0
0 0 -1 0 1 -1 1 -1 -1 0 0 1 0 1 0 -1 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0
-2-2 0 0 2 0-1 0 1 1 1 1-1 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0-1 0 0
-1 -1 1 0 0 1 0 1 0 0 0 -1 0 -1 0 1 0 1 -1 0 1 0 -1 0 0 0 1 1 0 -1 0 0
32 32
0 -1 2 0 -3 2 -3 1 2 0 -1 -2 1 -1 -1 1 1 1 -2 0 3 1 -1 0 -2 2 2 2 2 0 0 0
0 1 -1 0 3 -3 2 0 -2 -1 0 1 -2 1 1 0 -2 0 1 0 -2 -1 1 0 2 -2 -2 0 -2 0 0 0
0 -1 0 0 -2 1 0 1 1 1 0 -1 0 -1 0 0 1 1 1 -1 1 0 0 0 -1 1 2 0 0 0 0 0
0 0 0 0 -1 1 -1 -1 1 0 0 0 1 0 -1 0 1 0 -1 0 1 0 0 0 -1 1 0 0 2 0 0 0
0 0 0 0 -1 0 -1 1 1 0 -1 -1 0 0 -1 0 1 0 -1 -1 2 0 -1 -1 -1 2 1 1 1 -1 1 -1
0-1 0 1 0 1 1-1 0 1 0 1 0 1 0-2 1 0 1-2 0 1 1 1-2-1 0-1
0 -1 1 0 -1 2 -1 0 1 1 1 0 1 -1 0 0 0 0 -1 1 0 1 0 0 0 0 1 0 0 0 -1 0
0 -1 1 0 -1 2 -1 0 1 1 1 0 1 -1 0 0 0 -1 -1 1 -1 1 0 0 0 0 1 0 0 0 -1 0
0 1 0 0 1 -1 0 1 0 0 0 0 -1 0 0 0 0 -1 0 0 -1 0 0 -1 1 0 0 0 -1 0 0 -1
2 2 -1 0 0 -3 2 0 -1 -1 -1 -1 -1 2 0 -1 0 0 1 -1 0 0 0 -1 -1 0 0 0 1 0 1 0
0 0 1 0 0 0 -1 1 0 -1 -1 -1 0 0 0 1 0 0 -1 0 2 0 -1 0 -1 1 0 1 0 0 1 0
1 0 0 0 -1 -1 0 0 0 0 1 1 0 0 1 0 -1 0 1 1 -3 1 2 1 1 -2 0 0 -1 1 -1 1
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0 0 1 0 0 1 -1 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 1
2 3 -2 0 1 -5 3 0 -2 -1 0 1 -2 2 1 -1 -1 0 3 0 -3 0 2 0 1 -2 -1 -1 -1 1 0 0
1 1 1 0 -1 -1 -1 0 0 -1 -1 -1 0 1 0 0 0 0 0 0 0 1 0 0 -1 0 0 1 1 1 0 1
1 0 1 -1 -3 1 -3 0 1 0 -2 -1 1 -1 -2 0 1 0 -2 1 2 1 -1 0 -1 1 1 1 2 0 0 0
1 -1 -1 -2 -1 0 -1 0 0 0 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0-1-1-1 0 1-1 0 1 1 1-1 0 0 0 0 0 0 0 0 0 0 0 0 0-1 0 0 0 0 0 0 0
0 1 -2 0 3 -3 5 0 -3 -1 1 1 -1 2 2 0 -1 1 2 -1 -1 -1 1 0 0 -1 -1 -1 -1 -1 1 0
0 1 2 1 0 0 -1 2 0 -1 0 -1 0 1 1 1 0 -1 -1 1 0 1 0 0 0 0 0 1 0 0 0 0
32 32
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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1 -1 -1 -1 -1 0 -1 -1 1 1 0 1 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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1 1 0 0 0 -1 0 0 0 0 -1 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 2 1 1 1 -1 1 1 -1 -1 0 -1 -1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 -2 -1 -1 -1 1 -1 -1 1 1 0 1 1 -1 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 -1 -1 -1 -1 0 -2 0 1 1 -1 1 0 0 -1 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 -1 -1 -1 -1 0 -2 0 1 1 -1 1 0 0 -1 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
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0 -1 0 0 0 1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
32 32
0 -2 -1 -1 0 1 0 -1 0 0 0 1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0-2-1-1 0 1 0-1 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 0 0 0 0
1 -1 -1 -1 -1 0 -1 0 0 -1 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 2 1 1 0 -2 0 0 0 0 -1 0 -1 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 -1 -1 -2 -2 0 -1 -1 1 1 -1 0 0 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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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
0 -2 -1 -1 0 1 0 -1 0 0 -1 0 0 -1 0 0 0 1 0 0 1 -1 -1 0 0 0 0 0 0 0 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
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0 0 1 0 0 1 -1 1 0 -1 -1 -2 0 0 0 1 0 0 -1 0 1 0 -1 0 0 0 0 1 1 0 0 0
0 -1 -2 0 0 -1 1 0 0 0 1 1 0 0 1 -1 0 0 2 0 -2 0 1 0 1 -1 0 -1 -1 0 0 0
0 0 0 0 0 0 0 1 -1 -1 1 1 1 0 1 1 0 0 0 1 0 1 1 1 -1 0 0 0 0 0 0 0
0 0 0 0 2 -1 2 0 -2 -1 0 0 -1 1 1 0 -1 1 1 0 -1 0 0 0 0 -1 0 0 0 0 0 0
0 0 0 0 2 -1 2 0 -2 -1 0 0 -1 1 1 0 -1 2 1 -1 1 0 0 0 -1 0 0 0 0 0 0 0
2 2 0 0 -1 -3 1 1 -1 0 0 0 -1 1 1 -1 -1 0 1 1 -2 1 1 0 0 -1 0 0 -1 0 0 0
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1 0 0 0 -1 -1 1 0 0 -1 -1 -1 -1 0 0 0 0 1 1 0 0 0 0 0 -1 0 1 0 0 0 0 0
0 2 1 1 1 -1 0 1 0 -1 1 0 0 1 1 1 0 -1 0 0 -1 1 1 0 0 0 0 0 0 1 0 0
2 2 -1 1 -1 -3 1 1 0 -1 0 0 0 2 1 -1 0 0 1 0 -1 1 1 0 -1 0 0 0 0 0 1 0
2 1 0 0 -1 -1 1 0 -1 0 -1 -1 -1 1 0 -1 -1 1 1 0 -1 0 0 0 0 -1 0 0 0 0 0 1
32 32
1 2 0 0 0 -2 0 1 -1 0 -1 0 -1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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1 0 -1 -1 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 0 0
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0 -1 -1 -1 -1 1 0 0 0 1 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -1 -1 0 -1 1 0 0 1 1 1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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1 -1 -2 -1 0 0 0 0 0 1 0 1 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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1 2 1 0 0-1-1 0-1 0 0 1-1 0 0-1-2 1 0 0 0 0 0 0-1 0 1 0 0 0 0 0
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0 0 1 0 -1 0 -2 2 0 0 -1 -1 0 0 0 0 0 1 -1 0 2 1 -1 0 -1 1 1 2 1 0 0 0
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-1 0 2 0 0 2 -2 0 1 0 -1 -1 0 -1 -1 1 0 0 -2 0 2 0 -1 0 0 1 0 1 0 0 0 0
0 0 -1 -1 1 0 0 -1 0 1 -1 1 -1 0 -1 -1 0 -1 1 0 -2 -1 0 0 2 -1 -1 -1 -1 0 0 0
1 1 0 0-2 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1-1 0 1 0 0 0 0 0 0
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1 2 1 0 -1 -3 0 1 -1 -1 -1 0 0 1 0 0 0 0 0 1 0 2 0 0 -1 0 1 1 0 0 0 0
-1 -1 -1 0 2 0 2 0 -1 0 1 0 -1 0 1 0 0 0 2 -1 -1 -1 0 0 1 -1 0 -1 -1 0 0 0
1 3 2 1 0 -3 0 1 -1 -2 -1 -1 -1 2 0 0 -1 0 -1 1 0 1 0 0 -1 0 0 1 1 0 0 0
0 -1 0 -1 -1 1 -1 1 0 1 -1 -1 0 -1 0 0 0 1 0 0 1 0 -1 0 0 0 1 1 0 0 0 0
0 1 0 0 -1 -1 0 -1 1 0 0 1 0 0 -1 0 1 -1 1 0 -1 0 1 0 0 0 0 -1 0 1 0 0
-1 0 0 0 1 0 1 0 0 0 0 0 -1 0 0 0 1 0 2 -1 0 -1 0 0 0 0 0 -1 -1 0 1 0
-1 -1 0 0 1 2 0 0 -1 0 0 -1 1 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1
-
HERMITIAN_结构
4
32 32
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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32 32
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属性
模块化=1
UnimodularHermitian=1
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参考文献
Bachoc,Nebe:两类32维晶格的分类
超过赫尔维茨命令
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注释
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最后一行
Haftungsausschluss/免责声明
加布里埃尔·内布