Laminating lattices with symmetrical glue
| dc.creator | Elser, Veit | |
| dc.creator | Gravel, Simon | |
| dc.date | 2008-02-06 | |
| dc.date.accessioned | 2026-07-07T09:18:59Z | |
| dc.date.available | 2026-07-07T09:18:59Z | |
| dc.description | 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. | |
| dc.description | 14 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/0802.0730 | |
| dc.identifier | http://arxiv.org/abs/0802.0730 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154224 | |
| dc.subject | Metric Geometry | |
| dc.subject | 52C17; 52C23 | |
| dc.title | Laminating lattices with symmetrical glue | |
| dc.type | text |