《自然》杂志介绍填充问题研究中的新进展

（转自《科学时报》）

** **2009年8月13日《自然》杂志第460卷发表封面文章__《____Dense packings of the Platonic and Archimedean
solids____》__（柏拉图多面体和阿基米德多面体的最紧密堆积），介绍普林斯顿的师生在填充问题（__Packing problem__）研究中取得的进展。

基于致密颗粒堆积几何知识的模型，可帮助解释很多体系的结构，包括液体、玻璃、晶体、颗粒和生物体系。这一领域以前的研究工作大部分集中在球状颗粒上，但即使对这种理想化的形状，这个问题仍然极为困难——__Kepler____关于球体最紧密堆积的猜想__直到2005年才得到证明。人们对18个经典几何形状——柏拉图多面体和阿基米德多面体（如本期封面所示）——的最紧密排列知之甚少，虽然它们自古希腊时代以来就为人们所知了。现在，__Salvatore
Torquato__和__Yang Jiao__报告了5种柏拉图多面体（四面体、立方体、八面体、十二面体和二十面体）和13种阿基米德多面体的已知最紧密排列。这些多面体的对称性在决定它们基本堆积排列中非常关键，具有中心对称性的柏拉图多面体和阿基米德多面体的最紧密堆积被猜想由它们相应的最紧密（布拉菲）晶格堆积给出。

英文报道(from the __Princeton
University press release__)

**Princeton**** pair sets world record in packing puzzle**

Princeton researchers have beaten the present world record for
packing the most tetrahedra into a volume. Research
into these so-called packing problems have produced deep mathematical ideas and
led to practical applications as well. Princeton University/Torquato
Lab.

** **

"Finding the best way to pack the
greatest quantity of a specifically shaped object into a confined space may
sound simple, yet it consistently has led to deep mathematical concepts and
practical applications, such as improved computer security codes. When
mathematicians solved a famed sphere-packing problem in 2005, one that first
had been posed by renowned mathematician and astronomer Johannes Kepler in 1611, it made worldwide headlines. Now, two
Princeton University researchers [__Salvatore Torquato__,
a professor in the Department of Chemistry and the Princeton Institute for the
Science and Technology of Materials, and**
**__Yang Jiao__,
a graduate student in the Department of Mechanical and Aerospace Engineering]
have made a major advance in addressing a twist in the packing problem, jamming
more tetrahedra--solid figures with four triangular
faces--and other polyhedral solid objects than ever before into a space. The
work could result in better ways to store data on compact discs as well as a
better understanding of matter itself. __Henry Cohn__,
a mathematician with Microsoft Research New England in Cambridge,
Mass. says, 'the Princeton
researchers, have thrown out a new challenge to the
math world. Their results could be considered a 21st Century analogue of Kepler's conjecture about spheres. And, as with that
conjecture, I'm sure their work will inspire many future advances.'"