How can we manipulate the topological connectivity of a three-dimensional prismatic assembly to control the number of internal degrees of freedom and the number of connected components in it? To answer this question in a deterministic setting, we use ideas from elementary number theory to provide a hierarchical deterministic protocol for the control of rigidity and connectivity. We then show that it is possible to also use a stochastic protocol to achieve the same results via a percolation transition. Together, these approaches provide scale-independent algorithms for the cutting or gluing of three-dimensional prismatic assemblies to control their overall connectivity and rigidity.

中文翻译：

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棱柱组件中连接性和刚度的控制

我们如何通过操纵三维棱柱组件的拓扑连通性来控制内部自由度的数量和内部连接组件的数量？为了在确定性环境中回答这个问题，我们使用初等数论的思想来提供用于控制刚性和连通性的分层确定性协议。然后我们表明，也可以使用随机协议通过渗透转换实现相同的结果。总之，这些方法为切割或粘合 3D 棱柱组件提供了与比例无关的算法，以控制它们的整体连接性和刚度。