Space representations seem to be analogous to network representations. I used to think that visual patterns lead to the idea of space and layout but I think it's the other way around. Network representaions lead to patterns that can be represented visually.
Spatial
I think for the spatial we have a sense of proximity to features or nodes in a grid. I don't think we replicate all the movements that got us to a place but rather that we know how to move through space and we identify cues or signs about the place where we are at.
Grid Cells
The more I think about them the more they make sense. I just haven't figured out why a hexagonal pattern. What spatial properties do they have? In any case, what I'm figuring out is that each grid cell might represent a specific length of separation which could be triggered by senses. I'm still not sure about how they are wired up though. What I don't understand is why does the firing draw a lattice in a surface? Also, those same neurons could be triggered by time instead of distance. Maybe they are dynamically used as if they were some type of RAM?