A section of three dimensional space can be modelled as a cubic grid with nodes where the edges intersect, up to some limited resolution for a cube of finite volume ( and I suppose the same holds true with more than three dimensions ).
It sounds as if you’re proposing this graph basically be flattened—you take a fully connected regular polygon of n^3 angles, map the nodes in your cube to your polygon and then delete all edges in the connected polygon that don’t correspond to an edge present in the cube.
I have further questions but they hinge on whether or not I’ve understood you correctly., Is the above so far a fair summary?
A section of three dimensional space can be modelled as a cubic grid with nodes where the edges intersect, up to some limited resolution for a cube of finite volume ( and I suppose the same holds true with more than three dimensions ). It sounds as if you’re proposing this graph basically be flattened—you take a fully connected regular polygon of n^3 angles, map the nodes in your cube to your polygon and then delete all edges in the connected polygon that don’t correspond to an edge present in the cube.
I have further questions but they hinge on whether or not I’ve understood you correctly., Is the above so far a fair summary?