"Help me with my grid math" Topic

So in trying to design some gridded terrain tiles, I ran into a math dilemma my feeble skills cannot solve. I'm hoping one of you can help or at least provide some general guidelines.

I have terrain tiles that are 24" across, but really 22" across, because the last inch on any side is "shared" with the next board via the "teeth" that link them together.

I had hoped to put a 4" hex grid on each square tile, with the idea that you could put the tiles together in any order, as long as you kept the east-west "grain" of the hexes on each tile going the same direction.

With a 24" tile, that would be an easy 6 hexes across. However, I realized the shared space where the teeth joined up messed things up. And no matter how I adjusted the hexes (I was playing around with actual printed hexes), I could not configure a layout that wasn't ending up with some odd layout that prevented the square tiles from matching up (tesselate?)together with their hex grids intact.
Because I only use the center dot of the hex on the grid, I then tried to use offset squares, but alas, was also not up to the challenge.

So my question: Is it possible to put a 4 inch hex grid on 24" square tiles (remember with a 1" border that will be shared with the adjacent tile, so 22" square once you take out the border)? OR, what would the measurement be for offset squares/rectangles to achieve the same thing (it doesn't have to be exact, just something as close to 4" as possible)? The shared border is really messing up my attempts.

I'm sure there's some simple solution, but my mind tends to lock up when numbers flow through it, so any help from the non-geometrically challenged would be greatly appreciated.

Thanks!

Did you try centering a hex where 4 panels come together? Basically a 1/4 hex on 4 boards.

I have 2 foot panels marked out for GeoHex (12" hexes). The sides go 1/4 hex, 2 1/2 hexes, 1/4 hex flat side top to bottom. I have 2 hex by 2 hex panels but they are not square as the distance across the points is greater than the flats.

Try looking up "squexes" on TMP. That way you can use (offset) squares instead of hexes.

So my question: Is it possible to put a 4 inch hex grid on 24" square tiles

You do not have a 24" tile. Your 22" tile shares a 1" border with the next tile. That's 1/2" for your tile and 1/2" for the next tile. Do that on the right and on the left and you share 1" total. Thus your tile is effectively 23" (22+1/2+1/2=23).
23" / 6 = 3.8333" about 3 & 13/16ths". Something close to 4".
If you are only laying out center dots with a ruler and pencil the adjustment is easy. The pattern should repeat such that you can stack your tiles and drive a small nail through them to mark the set.

It seems like this would be very easy to draft up in AutoCAD. If you don't mind waiting a bit I will take this to the computer at home today and see what I can do

Do I understand correctly that you do not mind the Hex pattern being "broken" across the boarder?

Yes, you are correct, hexes and quadrilaterals (in this case, squares) have an irrational harmonic, so they won't line up.

Squexes is a way to approximate that. Here is an old wargaming paper on another approach. While the math is detailed and complex, the approach is simple to implement.

Victor -- yes, a little fudging along the border would be fine.

Etotheipi -- interesting paper, thanks for sharing. I'm going to look up more on squexes as zephyr mentioned to see what else I can learn.

OK -- only found one thread on squexes and it didn't really add anything beyond what I already know.

Etotheipi -- if I used your hex approach, how could I draw something that would yield approximately 4" hexes (flat side to flat side)? What size would the underlying grid have to be? (hope I'm understanding all this correctly)

Looking at the diagram on page 4, use a one inch underlying grid to make 4" flat to flat. If you assume the square grid is one inch, that diagram is actually what you would do. Put the "point" along the center line, one inch up and down from the ends of the flat sides.

You can fudge, especially if you are only using a small number of sheets. The advantage this approach for a modular board is you can increase or decrease the size of the modular pieces with no worrying about different fudging in different locations. So if you wanted to add a two hex wide river between two boards or superimpose a 3 hex diameter mountain or city facility on top of an existing grid, they would line up.

The cost is that they would only line up north=south or south-north, and you would not get precise alignment for a 60 or 120 degree rotation. The misalignment would be based on the small percentages on the area differentiation tables.

By my maths, a 3.833" hexagon should fit (97.34mm). It gives 6x6. You can make it as exact as you like, I don't think the difference between, say, 97 and 98 mm would be significant, but I would work symmetrically from the edges towards the centre, and make sure all the edges match.

Maybe make a cardboard tile or six as patterns.

Dagwood, as a guy who used to lay floor and ceiling tile, my advise would have been the reverse. The old hands told me to always start at a (carefully calculated) center and work out, with any fudging to be done on the borders. I'd suggest doing a tile or so with washable markers before doing anything permanent.

Ran several cad versions today, and there really is no way to "center" a set of true hexagons that measure 4 inches side to side, on a square board. If, on the other hand your base board was 24 inches wide and 24.25 inches tall, it would work. your base board would be seven hexes tall (staggered with half a hex at top and bottom) and six hexes wide.

But this all becomes useless when you try to introduce overlapping board connections which have a terrible effect on the hexagon arrangement at the overlap.

Thanks all -- very helpful as always.

I think technically your actual sizes are 23". What you lose on the North and East of each, you gain on the SOuth and west.

Could this be what is ruining your maths?