Comparing hexagons with squares: The ‘forgotten’ factor

Having convinced myself that I could get a larger number of grid areas on my mini-campaign board if I switched from hexes to squares, I sat down today to see if it was possible …


Look at the following photograph of my mini-campaign board.

Can anyone spot the very obvious (blindingly obvious … but not to me!) factor that I had forgotten?

Yes! You’ve got it! The 3’/90cm x 2’/60cm board has a frame! The hexes fit inside the frame … but the squares will not.

Just as final proof that it always pays to look properly at a solution before pursuing it, I drew a 9 x 6 squared grid over an 8 x 6 hexed grid, making sure that the face-to-face distances on the squares was the same as that of the hexes …

… and it doesn’t fit in the same space.

Serves me right for trying to find something to occupy my mind when I could not sleep!


22 Comments on “Comparing hexagons with squares: The ‘forgotten’ factor”

  1. At least you can work yours out. My insomnia inspirations take higher maths that I don't have…

    For example, last night I was considering the implications of 3D printing technologies, but applying it backwards where different materials are broken down to the atomic level and then rebuilt into something else using an advanced 3D printer.

    Apart from that, I was once a proponent of squares over hexes, but now I have reversed my position. I think I would prefer to see you continue with the portable wargame, at least including a hex variant.

    With Heroscape terrain pieces, the Hexon, and even GeoHex, there are reasonable options for gamers to choose from.

  2. nobby says:

    The answer, and the problem, are not contained in your first sentence, are they?
    …. a lager number of grid areas …..

  3. nobby says:

    Just a thought, which I think that you may have tried previously, but what happens if you turn the squares to make diamonds? Doesn't it give you a choice of three directions on a forward or reverse movement?

  4. Justin Penwith,

    It sounds like your insomnia has a more interesting edge to it than mine … and I suspect that the concept of 3D printing things like food at an atomic level will eventually come, although I don't know if I'd want to eat a 3D printed Big Mac!

    I am certainly going to stick with hexes for my future mini-campaign battles … and probably my larger battles as well. As I have enough Hexon II hexes to cover 9' x 8' tabletop it would be daft not to.

    All the best,


  5. Nobby,

    Lager? And I don't even drink! I really must proof-read what I type before pressing the 'Publish' button. Reading your comment made me realise that … and to correct the error. You are also right about the answer and the problem being encapsulated in the first sentence of my blog entry. I wanted to do something that was basically impossible.

    All the best,


  6. Nobby,

    If you use equilateral triangles rather than diamonds they will tessilate and might therefore be a possible alternative to hexes or squares … but as six equilateral triangles can be used to form a hexagon, I might as well stick to using hexes.

    I have seen diamonds used in a nineteenth century wargame, but the rules were more chess-like than most modern sets of wargame rules.

    All the best,


  7. There is one problem with squares that hexagons solve by their shape. Chessplayers will know this. On a Chessboard, an 8-square long diagonal has in effect the same distance as an 8-square orthogonal. The King can go from one corner to any other corner in 7 moves. That can have some weird and (from a chessplayer's point of view) wonderful effects.

    Desirable and interesting in chess, it creates a real topological problem for war games. My own solution has always been to use some kind of movement allowance system in which the ratio of diagonal to side length of a square is taken as 3/2. But gunnery ranges can prove problematic. I have some ideas about this, but I've not really put them to the test.

    I seem to recall discussing something of this on my blog a few years ago.

  8. phf says:

    Don't forget that there are two ways to lay out a hex grid.


  9. Dave C says:

    Another aspect to staggered squares which may be of interest:

    If the “squares” are actually rectangles, with the height of a row of squares equal to .86 x the width of the individual squares in the row, the diagonal distance is the same as the side-to-side distance.

    The distance advantages of hexes and the layout advantages of squares.

  10. Isn't the obvious solution just to use smaller squares? I was doing some gridded boards for Minschlacht and I found my carpet tiles were lightly too small for 75mm squares so I had to go with 66mm ones instead. It doesn't affect gameplay and just means the 'stuff' is slightly closer together.

    Diagonals with square grids can be treated in two ways, ignore them and only allow orthogonal movement, or do the calculations for movement points or whatever. Orthogonal actually works fine for linear periods of warfare as there is usually far too much wheeling going in in our games anyway, and it also works for high intensity combat (WW1 etc). Ranges are similar, make it orthogonal only, or reduce by .33 for diagonals. A very neat solution is that used in PBI – measure ranges orthogonally but allow a single diagonal to be included. As long as your ranges aren't too long the maths works out about right and it has the benefit that 'range 1' can include all the adjacent squares.

  11. Archduke Piccolo,

    I know exactly what you mean … and it is one reason why I tend to prefer hexes over squares. In the past I have tried using a movement points system (i.e. 'giving' a unit 6 movement points and it 'costing' 2 points per square of orthogonal movement and 3 for diagonal movement) which players had no problem using … but transferring the idea over to weapon ranges just did not seem to work as well. It sounds as if you ran into the same problem.

    I suspect that there might be a solution to this … but at present I cannot see one.

    All the best,


  12. Phf (Howard),

    Quite true … but it did not work for me when I used my Hexon II hexes on my mini-campaign board. If I wasn't trying to use the latter, it would certainly be a solution.

    All the best,


  13. Dave C,

    I'd have to look at your suggestion in greater detail, but it sounds as if you might have hit upon a workable solution to one of my objections to staggered square grids. Thank you for sharing it.

    All the best,


  14. Martin Rapier,

    I must admit that I had considered using smaller squares but I then realised that the bases of the units I was using would not quite fit into them.

    I agree that squared grids seem to present fewer problems when used during historical periods when tactics demanded linear formations … and my recent battle involving my modular fortress proved exactly that.

    I have not used the PBI rules, but have heard about their 'one diagonal' rule for weapon ranges. It sounds as if it makes sense, and overcomes the problem to a certain extent. It may not be perfect, but it has the advantage of being simple and easy to remember.

    All the best,


  15. Phil Dutré says:

    If you keep the face-to-face distance identical, your hexes are 87% of the area of the squares. So yes, not surprising they don't fit 🙂

    Anyway, why the obsession with squares? Using rectangles which are almost squares might solve your problem nicely. Visually, it's hardly noticeable, and for all practical purposes ruleswise and areawise, it doesn't matter much.

  16. Phil Dutré,

    In the middle of the night when one cannot sleep, one sometimes imagines that one has found a solution to an imagined problem. It is only when one sits down in the cold light of day and takes a serious look at one's ideas that one realises one was wrong. That is what I did … and it has sparked off quite an interesting discussion about hexed and squared grids.

    You are the second person to suggest using rectangles … and it is an approach that might well be worth greater study. In the meantime I am going to stick to using hexes … and I may well be ordering some more in the next few days.

    All the best,


  17. Phil Dutré says:

    BTW, being a big fan of Kallistra hexes myself, using half-hexes to fill up the holes at the sides virtually enlarges your playing area if you allow usage of these half hexes as well.
    I asked Kallistra specifically to cut a set of hexes in half for me, and they did that for a little surcharge.
    Whether you like the playability and/or visual appeal of half-hexes is another matter, off course 🙂

  18. Phil Dutré,

    I had not considered buying half hexes from Kallistra … but it is something that I ought to consider doing.

    Thanks for the suggestion,

    All the best,


  19. Norm says:

    Good shout on the half hexes.

    Reading 'grid' comments over the years, there seems to be a goodly proportion of people who recommend the square over the hex simply because it is easier to create a square grid rather than the more complicated hex grid. This then tends to lead to the next recommendation, which is to use off set squares to give a hex effect while keeping the ease of laying down squares.

    I am just highlighting that these are really two separate arguements …… Easy over which one is functionally better. I.e. If someone was giving away free hex mats and free square mats, which one would you choose?

    Hexon terrain on the face of it is not cheap, but over the years I have spent MUCH more on a variety of battlefields, from cloths to boards to mats.

    Budget is a very personal thing, but over the long term, Hexon might offer the better value.

  20. Norm,

    I am giving serious thought to buying some half hexes, especially if Kallistra will cut them to order.

    I think your question about what people would choose if given the choice between free hexed grids and free squared grids is a good one … and all things being equal, I would certainly choose hexes over squares.

    Like you I think that Hexon II is well worth the cost, and I know that since I bought mine I have fought more wargames than I previously managed using 'conventional' terrain cloths and polystyrene terrain boards. It is fast to set up and take down, easy to store, and far more robust that polystyrene terrain boards.

    All the best,


  21. Whiskers says:

    I have the same problem with my 4ft x 3 ft notive board. It's actually 46″ x 34″ useable area.
    Luckily it will – on the reverse side – just accept a “Commands & Colors” layout of 10cm hexagons

    I have bought a couple of 4ft x 3ft frameless notice boards and hinged them to make a 6ft x 4ft layout, but without the frame they are somewhat flimsy.

  22. Whiskers,

    I had not considered buying a 4' x 3' notice board … but I may well have a look at what Staples has to offer next time I visit a branch, especially if that size board is big enough to fit a C&C/Memoir '44 set up on it.

    Good luck with your hinged frameless boards.

    All the best,


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