Control of connectivity and rigidity in prismatic assemblies
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Updated: Nov 22, 2025

Structural Design and Manufacturing of a Cruiser Class Solar Vehicle
Published on: January 30, 2019
Gary P T Choi1,2, Siheng Chen1, Lakshminarayanan Mahadevan1,3,4
1John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA.
Abstract:
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.
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