Here's a little something to think about

[NotLKH]

Attached you'll see 4 different hexagonal layouts. See if you can develop conversion methods to intertranslate between each.

Of course, the Family Map doesn't have enough information to translate directly to the other three, so assume you know the index of the sector that the individual Family cell is in.

You don't have to make a 1 to 1 translation for each possability, you can daisy chain to translate, ie...

If you have a translation from Cell to Ring_Sector_Offset,
And a Translation from Ring_Sector_Offset to Family,
And a Translation from Family with Sector to Cell, then
that is more than enough. All you'd have to then do is get XYZ to one of those three, and any one of those three to XYZ, and you'd be able to go from 1 to all of them.

Now, the conversions from XYZ to Ring_Sector_Offset might be the hardest to do, so be creative in your strategies.

I'll post my solutions in a few days, so...

-Have Fun
-Lou