Three-periodic nets and tilings: minimal nets
Three-periodic nets and tilings: minimal nets
复制标题
DOI：
10.1107/s0108767304015442
复制
发表时间：
2004-11-01
影响因子：
1.8
通讯作者：
Yaghi, OM
中科院分区：
文献类型：
--
作者：
Bonneau, C;Delgado-Friedrichs, O;Yaghi, OM
Beukemann和Klee [Z.克里斯塔洛格（1992），201，37-51]已经被检查。七个粒子在重心坐标中发生碰撞并且自纠缠。其他八个都是自然的。其中五个是自对偶的，网是亏格3的P、G、D、H和CLP极小曲面的迷宫网。已经找到了十二种方法将立方体细分为更小的瓦片而不引入新的顶点。在原始胞元中具有一个顶点的这种平铺的对偶具有的网是最小网之一。没有冲突的最小网是均匀的。
The 15 3-periodic minimal nets of Beukemann & Klee [Z. Kristallogr. ( 1992), 201, 37-51] have been examined. Seven have collisions in barycentric coordinates and are self-entangled. The other eight have natural tilings. Five of these tilings are self-dual and the nets are the labyrinth nets of the P, G, D, H and CLP minimal surfaces of genus 3. Twelve ways have been found for subdividing a cube into smaller tiles without introducing new vertices. Duals of such tilings with one vertex in the primitive cell have nets that are one of the minimal nets. Minimal nets without collisions are uniform.