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First, have you looked at octogons carefully? The don't tesselate. That means they can't join up without gaps - there will be diamond-shaped holes at the corners (or squares to each side, depending on the alignment). Even if you ignore these, what you're left with is just a grid by any other name, and all the problems therein - diagonal speed boosts, for a start.
Second, the idea of unit facing just doesn't make sense at Civilization's scale. These are large groups of units controlling several square kilometers of terrain and skirmishing for a year plus at a time with a single order. At this level of abstraction, the Fortification mechanic neatly without opening up a bunch of locial holes.
I'm not trying to shoot you down completely. I can see where you're coming from, but there's a reason hex grids are the layout of choice for strategy games these days. Octagons are ultimately a square grid, with the problems that entails.
https://www.youtube.com/watch?v=Pypd_yKGYpA
Each era can consolidate a number of hex grids. At ancient era one 'civ vi' hex would be like that of a large number of hexes 6^6. With technology advances armies will get bigger, mobility will get more range and thus consolidating a ^1 per era or type of tech.
This would mean that ancient age would make the map larger as opposed to the industrial age etc... also the armies would fill up a larger grid. If an ancient age military, single unit group, came accross an industrial age single unit group the ancient age player would see an army of 6^4(or however many eras it takes to pass to industrial in that particular iteration of the game) sized army and the single ancient army would be 6^-4 by comparitive size naturally.
This would also be for districts sizes, farm and housing capacity and expansion of cities. The cultural influences would grow outwardly exponentially at higher eras as opposed to the earlier ones.
The only issue is making the balance fun because I can see where the tech gap, which is a main issue in this one, would be harder to enjoy due to the exponentially weaker civ in lower eras.
The concept is a rough idea but a good development team could make a good run with it.
This is roughly like the spore growth idea but without the horrid consolidation of actual gameplay. The expanding map would end up meeting a size that would be what our current size is grid by grid.
I wish I could mod something like this but this would be a core feature and cannot be modded into it as it stands currently.
Just an idea that has its strengths and weaknesses I am sure.
Sounds interesting to say the least. Not sure the current dev team would do a decent job tho. Look how they have flopped so far even with simple things. :(