The Gedanken Ball-and-Stick Construction Problem: What is the Most Simple Structure that it is Possible to Construct?

A very simple question is posed: Employing a ball-and-stick modelling system, and given a supply of the component balls and rods, then, treating it as a gedanken experiment, what is the most simple structure that it is possible to construct?
Keywords Foundations of mathematics  Structure  Fundamental underlying structure
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