具有对称胶的层压网格
Laminating lattices with symmetrical glue
摘要：
我们使用的自同构群$Aut(H)$，在晶格$L_8=A_2\oplus A_2\oplus D_4$中的孔，作为在10和12维的球体包装建设的起点。第二个格$L_4=A_2\oplus A_2$进入构造，因为$Aut(L_4)$的子群同构于$Aut(H)$。当通过这种关系胶合在一起时，晶格$L_8$和$L_4$提供了具有对接数648的12维叠层晶格的替代构造。更有趣的是，$Aut(H)$对$L_4$的作用定义了一对不变平面，通过这些不变平面可以构造10维的密集非晶格填充。其中最对称的是中心密度为1/32的非周期性。这些结构是由搜索算法发现的378个接吻球的意外排列引起的。
英文摘要：
We use the automorphism group $Aut(H)$, of holes in the lattice $L_8=A_2\oplus A_2\oplus D_4$, as the starting point in the construction of sphere packings in 10 and 12 dimensions. A second lattice, $L_4=A_2\oplus A_2$, enters the construction because a subgroup of $Aut(L_4)$ is isomorphic to $Aut(H)$. The lattices $L_8$ and $L_4$, when glued together through this relationship, provide an alternative construction of the laminated lattice in twelve dimensions with kissing number 648. More interestingly, the action of $Aut(H)$ on $L_4$ defines a pair of invariant planes through which dense, non-lattice packings in 10 dimensions can be constructed. The most symmetric of these is aperiodic with center density 1/32. These constructions were prompted by an unexpected arrangement of 378 kissing spheres discovered by a search algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
