Rationalizing Euclidean Assemblies of Hard Polyhedra from Tessellations in Curved Space,Physical Review Letters

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Rationalizing Euclidean Assemblies of Hard Polyhedra from Tessellations in Curved Space
Physical Review Letters ( IF 8.1 ) Pub Date : 2023-12-21 , DOI: 10.1103/physrevlett.131.258201
Philipp W A Schönhöfer ₁ , Kai Sun ₂ , Xiaoming Mao ₂ , Sharon C Glotzer _{1,

2,

3}

Affiliation

Entropic self-assembly is governed by the shape of the constituent particles, yet a priori prediction of crystal structures from particle shape alone is nontrivial for anything but the simplest of space-filling shapes. At the same time, most polyhedra are not space filling due to geometric constraints, but these constraints can be relaxed or even eliminated by sufficiently curving space. We show using Monte Carlo simulations that the majority of hard Platonic solids self-assemble entropically into space-filling crystals when constrained to the surface volume of a 3-sphere. As we gradually decrease curvature to “flatten” space and compare the local morphologies of crystals assembling in curved and flat space, we show that the Euclidean assemblies can be categorized as either remnants of tessellations in curved space (tetrahedra and dodecahedra) or nontessellation-based assemblies caused by large-scale geometric frustration (octahedra and icosahedra).

中文翻译：

从弯曲空间中的镶嵌合理化硬多面体的欧几里得装配

熵自组装受组成粒子的形状控制，但仅从粒子形状对晶体结构的先验预测对于除了最简单的空间填充形状之外的任何东西来说都是重要的。同时，大多数多面体由于几何约束而不是空间填充的，但这些约束可以通过充分弯曲空间来放松甚至消除。我们使用蒙特卡罗模拟表明，当约束于 3 球体的表面体积时，大多数硬柏拉图固体会自熵地自组装成空间填充晶体。当我们逐渐减小曲率以“展平”空间并比较在弯曲和平坦空间中组装的晶体的局部形态时，我们表明欧几里得组装可以归类为弯曲空间（四面体和十二面体）中的镶嵌的残余物或基于非镶嵌的由大规模几何挫败（八面体和二十面体）引起的装配。

更新日期：2023-12-22

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