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公司)和
尼尔·J·A·斯隆(njasloane@gmail.com)

上次修改时间：2014年7月18日星期五13:26:38 CEST

索引文件|缩写

此文件的内容

名称
尺寸
分流器
格拉姆
最小_形式
亲吻_编号
HERMITIAN_集团_订单
HERMITIAN_集团_发电机
HERMITIAN_结构
属性
参考文献
笔记
最后一行

• 名称
  24兰特
  

• 尺寸
  24
  

• 分流器
  2^12
  

• 格拉姆
  24 0
  6
  0 6
  0 0 6
  -3 3 3 6
  -3 1 1 3 4
  -1 -3 -1 -1 0 4
  -1 1 -3 -1 0 0 4
  0 -2 -2 -3 -2 2 2 4
  -3 1 1 3 2 0 0 -1 4
  -1 -3 -1 -1 0 2 0 1 0 4
  -1 1 -3 -1 0 0 2 1 0 0 4
  0 -2 -2 -3 -1 1 1 2 -2 2 2 4
  -3 1 1 3 2 0 0 -1 2 0 0 -1 4
  -1 -3 -1 -1 0 2 0 1 0 2 0 1 0 4
  -1 1 -3 -1 0 0 2 1 0 0 2 1 0 0 4
  0 -2 -2 -3 -1 1 1 2 -1 1 1 2 -2 2 2 4
  -3 1 1 3 2 0 0 -1 2 0 0 -1 2 0 0 -1 4
  -1 -3 -1 -1 0 2 0 1 0 2 0 1 0 2 0 1 0 4
  -1 1 -3 -1 0 0 2 1 0 0 2 1 0 0 2 1 0 0 4
  0 -2 -2 -3 -1 1 1 2 -1 1 1 2 -1 1 1 2 -2 2 2 4
  2 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
  0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
  0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
  -1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 2 2 4
  

• 最小_形式
  4
  

• 亲吻_编号
  3024
  

• HERMITIAN_集团_订单
  2^9 * 3^7 * 5 * 7
  

• HERMITIAN_集团_发电机
  三
  24 24
  -1 0 0 2 -1 0 0 1 -1 0 0 0 -1 0 0 0 -1 0 0 0 1 0 0 -1
  0 -3 -2 2 0 -2 -1 1 0 -1 0 0 0 -1 0 0 0 -1 0 0 0 2 1 -1
  -2 2 -1 -2 -1 1 -1 -1 0 0 -1 0 0 0 -1 0 0 0 -1 0 1 -1 1 1
  -2 0 0 -3 -1 0 0 -2 0 0 0 -1 0 0 0 -1 0 0 0 -1 1 0 0 2
  2 0 0 -1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 -1 0 0 1
  0 3 1-1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 2-1 1
  1-1 2 1 0 1 0 0 1 0 1 0 0 0 1 0 0 1 0-1 1-1
  1 0 0 3 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1-1 0 0-2
  -1 0 0 -2 0 0 0 -1 0 0 0 0 0 0 0 -1 0 0 0 -1 0 0 0 1
  0 1 2 -2 0 1 1 -1 0 0 0 0 0 1 1 -1 0 1 1 -1 0 -1 -1 1
  2 -2 -1 2 1 -1 0 1 0 0 0 0 1 -1 0 1 1 -1 0 1 -1 1 0 -1
  2 0 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 -1 0 0 -1
  -1 0 0 -2 0 0 0 -1 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 1
  0 1 2 -2 0 1 1 -1 0 1 1 -1 0 1 1 -1 0 0 0 0 0 -1 -1 1
  2 -2 -1 2 1 -1 0 1 1 -1 0 1 1 -1 0 1 0 0 0 0 -1 1 0 -1
  2 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 -1 0 0 -1
  0 0 0 -2 0 0 0 -1 1 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 1
  0 2 2 -2 0 1 1 -1 0 1 0 0 0 1 1 -1 0 1 0 0 0 -1 -1 1
  2 -2 0 2 1 -1 0 1 0 0 1 0 1 -1 0 1 0 0 1 0 -1 1 0 -1
  2 0 0 2 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 -1 0 0 -1
  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 0 -1 -1 1 0 0 0 0 0 1 1 -1 0 0 0 0 0 0 0 0
  0 0 0 0 -1 1 0 -1 0 0 0 0 1 -1 0 1 0 0 0 0 0 0 0 0
  0 0 0 0 -1 0 0 -1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0
  24 24
  3 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 1 -2 0 0 -1
  0 2 -1 1 0 0 0 0 0 0 -1 1 0 0 -1 1 0 0 -1 1 0 -1 1 -1
  -1 1 3 -1 0 0 0 0 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 1 -1 -2 1
  -1 0 0 2 0 0 0 0 -1 0 0 0 -1 0 0 0 -1 0 0 0 1 0 0 -1
  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 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 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 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 -1 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0
  0 -2 -1 1 0 0 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 1 0 0
  -1 1 -1 -1 0 0 0 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 1 0
  -1 0 0 -2 0 0 0 0 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 1
  -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 0 0 0 0 1 0 0 0
  0 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 1 0 0
  0 0 -1 0 0 0 0 0 0 0 0 0 1 -1 -1 1 0 0 0 0 0 0 1 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
  -1 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 -1 0 0 0 1 0 0 0
  0 -2 -1 1 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1 0 0 0 1 0 0
  -1 1-1 0 0 0 0 0 0 0 0 0 0-1 0 0 0-1 0 0 0 0 1 0
  -1 0 0-2 0 0 0 0 0 0 0 0 0 0-1 0 0 0-1 0 0 0 1
  2 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1-1 0 0 0 0
  0 2 0 0 0 1 0 0 0 0 -1 1 0 0 0 0 0 0 -1 1 0 -1 0 0
  0 0 2 0 0 0 1 0 -1 1 1 -1 0 0 0 0 -1 1 1 -1 0 0 -1 0
  0 0 0 2 0 0 0 1 -1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1
  24 24
  -1 0 0 -1 -1 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 -1 1 0 0 1
  0 0 1 -1 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 -1 1
  1 -1 -1 1 1 -1 -1 1 0 0 0 0 0 0 0 0 1 -1 -1 1 -1 1 1 -1
  1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 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 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 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 0 0 2 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 -1 0 0 -1
  0 0 -2 2 0 0 -1 1 0 -1 -1 1 0 0 0 0 0 0 -1 1 0 0 1 -1
  -2 2 2 -2 -1 1 1 -1 -1 1 0 -1 0 0 0 0 -1 1 1 -1 1 -1 -1 1
  -2 0 0 0 -1 0 0 0 -1 0 0 -1 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 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 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 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 0 0 0 1 0 0 0 0
  -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 0 0 0 0 0 0 0 0
  0 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0
  0 0 -1 0 0 0 0 0 0 0 0 0 1 -1 -1 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 0
  -3 0 0 -1 -1 0 0 -1 -1 0 0 0 -1 0 0 -1 -1 0 0 -1 2 0 0 1
  0 -2 1 -1 0 0 1 -1 0 -1 0 0 0 0 1 -1 0 0 1 -1 0 1 -1 1
  1 -1 -3 1 1 -1 -1 1 0 0 -1 0 1 -1 -1 1 1 -1 -1 1 -1 1 2 -1
  1 0 0 -2 1 0 0 0 0 0 0 -1 1 0 0 0 1 0 0 0 -1 0 0 1
  

• HERMITIAN_结构
  4
  24 24
  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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 0 0 0 1
  24 24
  0 1 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 0 0 0 0 0 0 0 0 0
  1 -1 -1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 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 0 0 0 0 0
  0 0 0 0 1 -1 -1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 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 1 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 0
  0 0 0 0 0 0 0 0 1 -1 -1 2 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 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 1 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 0 0 0 0 0 0 0 0 0 1 -1 -1 2 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 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 1 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 0 0 0 0 0 0 0 0 0 1 -1 -1 2 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 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 0-1 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 -1 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 1
  24 24
  0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 1 1 -2 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 0 0 0 0 0 0 0 0 0
  -1 1 0 -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 0 0 0
  0 0 0 0 -1 1 1 -2 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 0 0 0 0 0
  0 0 0 0 -1 1 0 -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 0 0 0 0 0 0 0 -1 1 1 -2 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 0
  0 0 0 0 0 0 0 0 -1 1 0 -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 0 0 0 0 0 0 0 -1 1 1 -2 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 0 0 0 0 0 0 0 0 0 -1 1 0 -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 0 0 0 0 0 0 0 -1 1 1 -2 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 0 0 0 0 0 0 0 0 0 -1 1 0 -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 0 0 0 0 0 0 0 -1 1 1 -2
  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 0 0 0 0 0 0 0 0 0 -1 1 0 -1
  24 24
  -1 1 1 -1 0 0 0 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 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 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
  0 0 0 0 -1 1 1 -1 0 0 0 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
  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 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 0 0 0 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 0-1 0-1 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 -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 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 1 1 -1 0 0 0 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 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 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 0 0 0 0 -1 1 1 -1 0 0 0 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 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 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 0 0 0 0 -1 1 1 -1
  0 0 0 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 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 0 0 0 -1 0
  

• 属性
  模块化=1
  

• 参考文献
  C.Bachoc，Voisinage au sens de Kneser pour les r \'eseaux四元数。
  注释。数学。Helvetici 70（1995），350-374。
  
  Bachoc，Nebe：两类32维晶格的分类
  超过赫尔维茨命令
  

• 笔记
  

• 最后一行
  
  
  

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