IMHO, any lateral force would make this collapse. Nodes 1234 indeed create a statically determinate body.
However, the rod 3-5 and 4-6 are parallel and of equal length. Therefore body 1234 can freely rotate.
Regarding how you show that mathematically, (without knowing the context of your assignment):
1234 is a rigid body
you can substitute 1234 with a ...
TL;DR: Real life equations are created by carefully observing relationships between different quantities, making simplification assumptions, and then abstracting them into a mathematical form.
I've posted below a few examples of how to derive DE's from "real life" examples for a range of sciences. Hopefully, they will give a glimpse of the process.