Half-Mile and Six-Mile Hex Cheat Sheet

I've always struggled with distance and scale in tabletop RPGs. I'm also...let's say "rusty" on my geometry, especially that of the hexagonal persuasion. Converting between different mapping scales is one of my biggest bugbears, as is the whole process of...you know, taking a real-world place or object and figuring out how to size it on a map, or conversely, looking at a map and picturing in my mind's eye how big or far it should be realistically. I'm exponentially worse at this with hexes than with squares.

Thanks to a very enlightening post at The Hydra's Grotto, I've grown fond of using 6-mile hexes for wilderness travel. Rereading that post the other day, I was struck by the idea of subdividing 6-mile hexes into half-mile ones, and after trying to sketch this out I realized I didn't know how to actually make that work - as in, how to fit the little hexes into the big hexes. After scouring the internet for a map or diagram demonstrating this technique, I resorted to just screwing around with some hex grid paper (courtesy of Imcompetech) until I figured it out. Well, at least I think I did. If there's a better way assemble these dang ol' hexagons can someone please let me in on the secret?

At that point, I took a few more notes, and now I think I've almost got my head wrapped around the problems mentioned above. This is probably "no duh" territory for a lot of people, but I personally found the whole exercise useful enough that I figured I should share my notes in case anyone else has been hexed by hexes like me. It would put a real smile on my face if I helped make the subject less intimidating for even one person.

Coming to D&D from a mix of 3rd Edition and various video games, I was slightly perturbed by the sudden influx of hex grids into my life when I started delving into older editions and OSR stuff. I've grown increasingly fond of hex maps over time, but I almost wish I could send posts like this back in time to myself circa 2013 or so and clear up the concepts that confused me the most.

Here's a side view, so you don't have to turn the image or your head/monitor.

Now I just need someone to explain THAC0 for the millionth time so that'll hopefully sink in.