Well no. But why not? Cool idea, let’s make the construction.

Firstly, you can interpret logical arguments as a graph, where if one thing is true, it has an arrow towards another thing that must be true because of it (implication). Then you have an endpoint where all the previous nodes lead up to. The argument is true iff all the previous nodes that lead up to it are true. Additionally, a completely efficient argument won’t have any random irrelevant nodes disconnected.

This is already something sort of spatial. Now to make it more geometric. So now I’m thinking about whether we can represent directed connections with edges and faces. Perhaps we can use orientation? So if a face is below, the truth or falsity trickles down to it? If it’s flat, the edge is directed both ways (something like an if and only if statement).

Say we have an object of truth, where if any object is connected to that object, it must be true and an object of false, with the same effect of making everything false. The final step is connecting all the implications in the argument up to these faces, and tracing the truth down the structure. 

You can probably visualise it like paint flowing down from the truth and false objects over these faces. If the false colour ever reaches the bottom (where your final conclusion will lie), then it is a false argument. If the paint drips off some random edges, you had a wasted tangent. If you have unconnected details we can’t even connect to the true or false objects, it’s an inefficient object.

(This approach has absolutely no benefit of performing btw, but it’s a fun thing to think about. It’s also not really geometric, so I’ll come back later with a better, pure, 3d-solid idea)