Hexagon Tiles: Like them, love them, or RAGGGEEEE!!!

I'm quite dubious over the idea of hexes to be honest. Both hexes and squares have their positives and their negatives, and the differences will define how the game plays. Neither hexes or squares will provide a complete solution to all the issues that need to be considered, so it is a case of choosing which system you favour more, and what you can and cannot live with.

Hexes are good for mapping outdoor environments, as they allow for easier creation of circular forms, which are more natural-looking than squares. However, hexes are less suited to tactical situations than squares. Hexes have issues with orientation as it makes a substantial difference which way the hexes are orientated, and it is considerably harder to form straight-line formations in hex-based combat.

Conversely, the opposite is true for squares. While maps are unrealistic and "blocky", with the fat crosses rather than squares being an adequate example, squares excel in tactical based situations. The orientation of the square has no effect on the battle, and it's much easier to mark the straight-line formations that were used in classic warfare tactics.

Ultimately, what this seems to come down to is that Civ V is changing from squares to hexes, because it is shifting away from the tactical warfare elements of the game to focus on more naturalistic outdoor environments and better graphics. I feel the devs are building a rod for their own backs in this case, as they are introducing many issues in tactical situations that come primarily from using a hex-based system rather than the traditional square-based one. issues that tactical situations that didn't exist in previous incarnations of Civ for the very reason it used square-based maps.

I'm not entirely sure all these factors have been considered with the shift to hexes. More natural-looking outdoor environments is not a good excuse to detract from the tactical elements of the game, as Civ has always had a long tradition of focusing on gameplay over graphics, contrary to the other ideas on game design theory. Aesthetics is important, but not to the point where eyecand actively reduces other aspects of the game.

So, I'm kind of hesitant about the shift to hexes from squares in Civ IV. No doubt that many of the other features that the game will inevitably be hailed for could be modded into Civ IV and it's square-based maps anyway.

Also, the Atomic Gamer preview of Civ IV is incorrect in it's assumption the strategy is increased in Civ IV because of it's switch to hex-based maps. Hexes may have six faces to defend, but squares have eight, not four, as you can attack diagonally as well. This means that, in fact, the area surrounding a city in which opposing units can attack has been reduced, not increased, and thus makes cities (or, indeed, any hex, for that matter) much more defensible, which is not neccessarily a good thing when so many factors already favour the defender, and defending ultimately makes for boring gameplay.

The "cheating" of diagonals is easily remedied by applying a little trigonometry to the situation. Diagonal movement represents roughly 1.5 times horizontal or vertical movement. Simply mod in this ratio and the problem of "diagonal cheating" is basically solved. However this same "diagonal cheating" is part of the flaws that squares have, but is clearly matched by the hex-based flaw that units end up staggered by up to half a hex in some directions. Both issues provide this flaw in 4 of the possible directions, but squares provide accuracy in 4 other directions, where hexes only do so in 2.
 
I'm quite dubious over the idea of hexes to be honest. Both hexes and squares have their positives and their negatives, and the differences will define how the game plays. Neither hexes or squares will provide a complete solution to all the issues that need to be considered, so it is a case of choosing which system you favour more, and what you can and cannot live with.

Hexes are good for mapping outdoor environments, as they allow for easier creation of circular forms, which are more natural-looking than squares. However, hexes are less suited to tactical situations than squares. Hexes have issues with orientation as it makes a substantial difference which way the hexes are orientated, and it is considerably harder to form straight-line formations in hex-based combat.

Conversely, the opposite is true for squares. While maps are unrealistic and "blocky", with the fat crosses rather than squares being an adequate example, squares excel in tactical based situations. The orientation of the square has no effect on the battle, and it's much easier to mark the straight-line formations that were used in classic warfare tactics.

Ultimately, what this seems to come down to is that Civ V is changing from squares to hexes, because it is shifting away from the tactical warfare elements of the game to focus on more naturalistic outdoor environments and better graphics. I feel the devs are building a rod for their own backs in this case, as they are introducing many issues in tactical situations that come primarily from using a hex-based system rather than the traditional square-based one. issues that tactical situations that didn't exist in previous incarnations of Civ for the very reason it used square-based maps.

I'm not entirely sure all these factors have been considered with the shift to hexes. More natural-looking outdoor environments is not a good excuse to detract from the tactical elements of the game, as Civ has always had a long tradition of focusing on gameplay over graphics, contrary to the other ideas on game design theory. Aesthetics is important, but not to the point where eyecand actively reduces other aspects of the game.

So, I'm kind of hesitant about the shift to hexes from squares in Civ IV. No doubt that many of the other features that the game will inevitably be hailed for could be modded into Civ IV and it's square-based maps anyway.

Also, the Atomic Gamer preview of Civ IV is incorrect in it's assumption the strategy is increased in Civ IV because of it's switch to hex-based maps. Hexes may have six faces to defend, but squares have eight, not four, as you can attack diagonally as well. This means that, in fact, the area surrounding a city in which opposing units can attack has been reduced, not increased, and thus makes cities (or, indeed, any hex, for that matter) much more defensible, which is not neccessarily a good thing when so many factors already favour the defender, and defending ultimately makes for boring gameplay.

How is it that squares are better for tactics than hexes? You can slip between units on the diagonal, with squares. You claim that six direction will favor the defender. Well then they'll just do something that favors the attacker, and that problem is solved. Like only having one unit be able to stand in a city. And it's already been stated that you should be fighting before they reach your cities, so if they reach your city then it's probably too late to save it and it doesn't matter if they can surround it for six units or eight. Also who cares if lines aren't perfectly straight? You claim this decision is all about aesthetics, but how is wanting perfectly straight lines not being all about aesthetics. Also, you want straight line tactics represented, but if units could slip through diagonals, then you wouldn't have straight lines because you'd have to have more units in those potential holes. A line of five units can block a NSEW advance, but to block a diagonal you suddenly need four more units, almost twice as many, to block that advance. Thus true straight line formations are not as likely with hexes, but actually having your formation mean something isn't possible with squares. The one things I don't (yet) understand with hexes, is if an archer can shoot 'on the diagonal' (see diagram). However with squares there's the question of if an archer can fire like a knight in chess moves, one up and two over, which doing by diagonals is two moves. It should be possible, but it seems strange due to the inconsistant distance.
I'm not sure where this idea of there being many issues with hexes comes from, especially since it's pretty much established that serious war games use hexes, not that I ever believe that just because everyone says something it is true, but this is the first time I've ever heard the opposite.
 
I feel the hexes are a much needed improvement, for the reasons already mentioned.
I think units will be able to fire on any square they can move to in two moves or less. It would make sense anyway.

As for the hexes being an aesthetic impovement only, that is the only reason I would want squares. It's almost like the decimal numeral system. We know other options might make more sense, but we will probably never be able to change it(imagine being the generation having to make the change).
 
Well, it depends on the grain of the hex-grid. Either direct North-South or direct East-West will not be allowed in one move.

BTW, Love 'em.
 
Combat almost always favors the defender. Being able to fortify, use choke-points, and pretty much be ready for the attack makes defending favorable to attacking, at least in the eyes of the combatants.
 
I'm looking forward to the hexes, the added realism will be much fun... 'Sides it will be interesting to try out and try some new battle strategies
 
The thing with hexes is that it matters which way around the hex is. A hex has six sides, two of which are either north and south or east and west. Depending upon which way around the hex is, you get flanks that have either two or three adjacent edges. This means a front that is horizontal will be different from a front that is vertical.

However, with squares, the orientation of the square does not make a difference. Horizontal and vertical fronts behave exactly the same way. More importantly, each of the 8 cardinal directions is adjacent to three other squares, even diagonals.

The solution to stopping the issue of enemies slipping through to gaps in a diagonal is to set up a staggered front filling in those gaps. This staggered diagonal front is no different from thw staggered front you get with using hexes.

In fact, a square produces four diagonal directions, and 4 non-diagonal directions. Hexes, however, only provide two non-diagonal directions, but keeps the four diagonal ones.

Hexes are slightly better at handling diagonals, but this comes at the expense of being worse at handling non-diagonals. This means that the change can create as many problems as it solves.

Meanwhile, a simple solution with square grids is often ignored in such arguments - you can always orientate a square grid so that it is lined up with the situation at hand. If you rotate a square grid 45 degrees in any direction, the diagonals and non-diagonals swap places, and the issues with your diagonal front are now solved, simply because it is no longer a diagonal front. You try the same trick with hexes, and you will still get issues with staggered fronts.

Ultimately though, neither squares or hexes are going to be 100% realistic. Both will be flawed, and each will provide their own issues. For squares, you get the issues of diagonals, but you get the fact that orientation doesn't matter, straight fronts, and all sorts of other things that help relate to tactical situations. With hexes, you get the opposite, with better mapping capability, and reduced issues with diagonals, but orientation matters and straight fronts are gone resulting in unprotected flanks.

What is going to happen is that the issue of diagonal attacks on a square-based grid will be replaced with trying to make sure you can attack from the front which has three exposed sides rather than two, leading to a lot of north-south or east-west clashes based on the orientation of the hexes (it's hard to tell the orientation from the screenshots).
 
I'm looking forward to working out what's better AND worse about hexes, and enjoying the change from CivIV because of it. Or, more probably, waiting until someone with more time to play works it all out, then surfing the forum for the shortcuts.
 
No, you do not get the same issue with staggered fronts, I specifically mentioned that you need almost twice as many unit on a grid then a hex map to guard a diagonal. I made a diagram! I don't know what this obsession with straight lines is, but if you don't like the north south being curvy, tilt your head. Most of the problems you see with hexes I just want to ask, so what? I don't know how these things are to have dire consequences. And to reiterate my previous point (supported by diagrams), with hexes five units can block any direction without holes, with a grid 5 units can block one of four directions, then you need 9 to block by the diagonal. That is more, and not good. Hexes solve many problems, and I don't know what exactly are the problems it creates, or why they are worse.

The thing with hexes is that it matters which way around the hex is. A hex has six sides, two of which are either north and south or east and west. Depending upon which way around the hex is, you get flanks that have either two or three adjacent edges. This means a front that is horizontal will be different from a front that is vertical.
And diagonals are different then tiles joined by an edge. Why is that better?
However, with squares, the orientation of the square does not make a difference. Horizontal and vertical fronts behave exactly the same way. More importantly, each of the 8 cardinal directions is adjacent to three other squares, even diagonals.
The orientation is very important because of diagonals. Horizontal and vertical behave the same way. That is two directions, hexes have three directions that behave the same way. How is that not better?
The solution to stopping the issue of enemies slipping through to gaps in a diagonal is to set up a staggered front filling in those gaps. This staggered diagonal front is no different from thw staggered front you get with using hexes.
It is different because you need more units with a grid.
In fact, a square produces four diagonal directions, and 4 non-diagonal directions. Hexes, however, only provide two non-diagonal directions, but keeps the four diagonal ones.
And four or eight directions is better than six why? The reason the number 10 is important is because we have ten fingers. It's arbitrary and it's always been that way so we can't think any other way. Same with thinking eight directions is better than six. It's better because we think it's better, but it's not really significant.

Hexes are slightly better at handling diagonals, but this comes at the expense of being worse at handling non-diagonals. This means that the change can create as many problems as it solves.
I don't know what this fatal flaw is dealing with non-diagonals.

Meanwhile, a simple solution with square grids is often ignored in such arguments - you can always orientate a square grid so that it is lined up with the situation at hand. If you rotate a square grid 45 degrees in any direction, the diagonals and non-diagonals swap places, and the issues with your diagonal front are now solved, simply because it is no longer a diagonal front. You try the same trick with hexes, and you will still get issues with staggered fronts.
Rotating a grid 45 degrees is not the same, because of the diagonals.
Ultimately though, neither squares or hexes are going to be 100% realistic. Both will be flawed, and each will provide their own issues. For squares, you get the issues of diagonals, but you get the fact that orientation doesn't matter, straight fronts, and all sorts of other things that help relate to tactical situations. With hexes, you get the opposite, with better mapping capability, and reduced issues with diagonals, but orientation matters and straight fronts are gone resulting in unprotected flanks.
You only have two possible straight fronts with squares and three possible with hexes. How is it creating unprotected flanks, and how is that worse than diagonal holes in fronts requiring many more units?
What is going to happen is that the issue of diagonal attacks on a square-based grid will be replaced with trying to make sure you can attack from the front which has three exposed sides rather than two, leading to a lot of north-south or east-west clashes based on the orientation of the hexes (it's hard to tell the orientation from the screenshots).
You're complaint seems to be that north of a city there are only two hexes up against it so you can't use three units. Well what about the one to the west or east of the city? Use that one? Is it that it would take another move for a units to go there? Well have that unit move one step further when you leave home. If you were approaching from the diagonal on a grid, then the two outer units would have to move one more tiles to be to the north and west of a city, and the meddle would be on the diagonal first. Why would moving those two units differently be better than moving one with hexes?
 
Hexes for the win - but only when combined with the one unit per tile limit. Otherwise it is six of one, half dozen of the other. . .

While it is true that you cannot create a sphere out of hexes, you can certainly come a lot closer than you can with squares.

As for straight fronts. . .well, we never had fronts at all in Civ IV, so I will take the 3 possible axes in Civ V and love it. Trying to create a straight front against the grain will result in "peaks" - units that can be attacked by 3 opposing units, and "valleys' - units that can only be attacked by one enemy unit. Of course, they create tactical problems for the would be attacker, as well, since they would have to move into position to attack the defender's "peaks" - and would be vulnerable to being attacked by 3 defending units for their trouble.

I expect a typical defensive position would involve a staggered line of strong attacking units alternating with strong defending units, with the strong defenders being exposed on three sides. Place a range-capable unit behind each in the second line - enemy units moving up to attack the exposed units on three sides would find themselves facing up to 3 ranged attacks and the very teeth of the defender's offensive strength.

Hopefully that is where cavalry will shine - pushing through the gaps made by beaten defenders, or retreating after moving into exposed positions to press the assault.

Sounds much more tactically interesting than "Which unit in my stack do I want to throw against their stack?".
 
No, you do not get the same issue with staggered fronts, I specifically mentioned that you need almost twice as many unit on a grid then a hex map to guard a diagonal. I made a diagram! I don't know what this obsession with straight lines is, but if you don't like the north south being curvy, tilt your head. Most of the problems you see with hexes I just want to ask, so what? I don't know how these things are to have dire consequences. And to reiterate my previous point (supported by diagrams), with hexes five units can block any direction without holes, with a grid 5 units can block one of four directions, then you need 9 to block by the diagonal. That is more, and not good. Hexes solve many problems, and I don't know what exactly are the problems it creates, or why they are worse.

The fronts are still staggered, regardless of the amount of units used. More importantly, the entire issue with sneaking through diagonals is an artefact of using a square-based grid, that can be solved easily enough using the square-based grid as well. Most games give units a "control" radius that represents an area which the unit can engage other opponents passing by. Civilization lacks this feature, but if it was implemented, there would be no more issues with diagonal fronts in square-based grids. Another thing to bear in mind is that fronts are rarely a single rank, but often a formation of multiple ranks. Thus, regardless of whether you are using hexes or squares, the second line will commonly be filled, and thus sneaking through diagonals would be a non-issue on a square-based map.

As for straight fronts. . .well, we never had fronts at all in Civ IV, so I will take the 3 possible axes in Civ V and love it. Trying to create a straight front against the grain will result in "peaks" - units that can be attacked by 3 opposing units, and "valleys' - units that can only be attacked by one enemy unit. Of course, they create tactical problems for the would be attacker, as well, since they would have to move into position to attack the defender's "peaks" - and would be vulnerable to being attacked by 3 defending units for their trouble.

It should be noted that the mechanics of a single unit per space and hexes are not linked. Signle unit mechanics would work equally well in hexes or squares, with pretty much the same ramifications.

And diagonals are different then tiles joined by an edge. Why is that better?

There are currently no mechanical effects from attacking from a diagonal square compared to attacking from an edge square. Thus, in this regard, there is no difference at all. This means that each space in a front has exactly the same number of possible attacking positions, regardless of orientation. It doesn't matter that the attack is coming from the north, the east, or the north-east.

The orientation is very important because of diagonals. Horizontal and vertical behave the same way. That is two directions, hexes have three directions that behave the same way. How is that not better?

It's not better because squares have four directions, not two, since diagonals are not differentiated from edges. The issues of sneaking through diagonals is solved by adding more units - units that would form a second rank anyway, regardless of whether squares or hexes are used. Thus, diagonals and edges are the same in virtually all respects.

And four or eight directions is better than six why? The reason the number 10 is important is because we have ten fingers. It's arbitrary and it's always been that way so we can't think any other way. Same with thinking eight directions is better than six. It's better because we think it's better, but it's not really significant.

This is a non-arguement. Other base systems, such as binary and hexadecimal, have their routes in their functions as well, as both are computer based arithmetic systems. Likewise, time uses base 60 for seconds and minutes, because this is better for use on circular clock faces, and dealing with aspects of circles and rotations. Each different method of counting is better for a specific purpose only. Likewise, hexes versus squares - both have their uses. However, hexes are typically better for mapping purposes than strategy, because they allow for easier circles and other natural geographical formations. Most games that use hexes have always emphasised their aesthetics, and adaptred their tactical elements to fit, rather than the other way around.

Rotating a grid 45 degrees is not the same, because of the diagonals.

You seem to have misunderstood the point of this solution. You rotate the grid 45 degrees, so that a diagonal front is now aligned to a horizontal front. Units in grids are arbitrary, as they are not exactly placed within the grid, but considered centered (hence the slipping through diagonals issue). Thus, on rotation, such units would re-center themselves in their new squares. The gaps close along the new horizontal front, and open along the new diagonal ones. This is not shifting of units, but shifting of the modelling method used to represent the units on the battle field.

I don't know what this fatal flaw is dealing with non-diagonals.

Distances in the non-diagonal directions are skewed. While you can move in one non-diagonal direction (Say, north-south for example), the front is actually staggered by half a rank in adjacent hexes, so an east-west divide will pass through the centre of some hexes, and along the edges of adjacent edges. This is slighly more significant than a diagonal divide crossing points in a diagonal front, and rotation to orientate the grid to such features solves this completely.

Conversely, in the other non-diagonal direction (east-west in this example) the distance is easier to measure by counting the ranks, but troops cannot travel in a straight line in this direction. To do so would put them spread over two hexes.

In addition, if regular hexeagons are used for mapping, then the diagonals are not truly diagonals at all - they have a bearing of 60 degrees, not 45 degrees. So, you can't even accurately mark movement in these diagonal directions accurately without getting the same issues. However, virtually all hexagons with paralelle sides tesselate, so hexes for mapping are usually not regular, to allow for this diagonal movement to be accurately covered.

You're complaint seems to be that north of a city there are only two hexes up against it so you can't use three units. Well what about the one to the west or east of the city? Use that one? Is it that it would take another move for a units to go there? Well have that unit move one step further when you leave home. If you were approaching from the diagonal on a grid, then the two outer units would have to move one more tiles to be to the north and west of a city, and the meddle would be on the diagonal first. Why would moving those two units differently be better than moving one with hexes?

My complaint is that the north of the city should not inherently be any different to the east of the city. Nor should it be inherently different from the north-east of the city. With grids, orientation does not matter, particulalry since diagonal attacks are not differentiated from non-diagonal attacks. No matter what direction you attack from, you can attack and be attacked from three opposing squares.

This is not the case with hexes, which is why you have to specify the orientation of the hex grid in the first place. Rotating the grid by 90 degrees gives you essentially a different map with a different tactical arrangement. Rotating a grid by 90 degrees does not have this effect.

This issue, I feel, is much more significant than the issue of slipping through diagonals. More importantly, the slipping through diagonals issue is moot when it comes to city defence, simple because city capture requires you to enter the space, not slip past it, and if you are building a diagonal front on a square grid, you should at least have the foresight to position a unit in the city in the first place.

In the case of hexes vs. squares, this seems much more like change for change's sake, to make Civ V radially different from earlier Civ games without going into RTS or SimCity type gameplay. It's evident that square-based systems have not been fully exploited in the Civ series - there's still more that could be done with them, including one unit per square to allow the creation of fronts over stacks in the first place. However, hexes do represent an improvement in the ability to map overland geographical areas, and I cannot help but feel that the switch to hexes has been undertaken more for aesthetic reasons than tactical gameplay ones.
 
I expect a typical defensive position would involve a staggered line of strong attacking units alternating with strong defending units, with the strong defenders being exposed on three sides. Place a range-capable unit behind each in the second line - enemy units moving up to attack the exposed units on three sides would find themselves facing up to 3 ranged attacks and the very teeth of the defender's offensive strength.

See now that sounds like an interesting new tactical situation, which I welcome.
 
The fronts are still staggered, regardless of the amount of units used. More importantly, the entire issue with sneaking through diagonals is an artefact of using a square-based grid, that can be solved easily enough using the square-based grid as well. Most games give units a "control" radius that represents an area which the unit can engage other opponents passing by. Civilization lacks this feature, but if it was implemented, there would be no more issues with diagonal fronts in square-based grids. Another thing to bear in mind is that fronts are rarely a single rank, but often a formation of multiple ranks. Thus, regardless of whether you are using hexes or squares, the second line will commonly be filled, and thus sneaking through diagonals would be a non-issue on a square-based map.
Civ used to have a zone of control system (in civ2 certainly, maybe also civ3 don't remember). It indeed dealt with sneaking through diagonal fronts, but also made movement very non-intuitive. Sometimes you would unexpectedly not be able to make a certain move because you missed some units ZoC.

If you are going to introduce ZoC system to fix this problem, the same system can be used to solve your issue with staggered fronts in a hex grid.

There are currently no mechanical effects from attacking from a diagonal square compared to attacking from an edge square. Thus, in this regard, there is no difference at all. This means that each space in a front has exactly the same number of possible attacking positions, regardless of orientation. It doesn't matter that the attack is coming from the north, the east, or the north-east.
Actually to make a diagonal front on a square grid, you need to stagger as well. The front of the stagger can be attack from three sides while the second line can be attacked one direction. Same "problem" as before.



In addition, if regular hexeagons are used for mapping, then the diagonals are not truly diagonals at all - they have a bearing of 60 degrees, not 45 degrees. So, you can't even accurately mark movement in these diagonal directions accurately without getting the same issues. However, virtually all hexagons with paralelle sides tesselate, so hexes for mapping are usually not regular, to allow for this diagonal movement to be accurately covered.
In trying to move along a 60 degree a sloped line on a square grid is also not possible. I don't understand this obsession of trying to move in North-South or East-West lines anyway. The actual route you take in civ will be much more influenced by the actual terrain then by the nature of the grid.

My complaint is that the north of the city should not inherently be any different to the east of the city. Nor should it be inherently different from the north-east of the city. With grids, orientation does not matter, particulalry since diagonal attacks are not differentiated from non-diagonal attacks. No matter what direction you attack from, you can attack and be attacked from three opposing squares.
All tiles neighbouring a hex will be equivalent, much more so than in a square grid.


This is not the case with hexes, which is why you have to specify the orientation of the hex grid in the first place. Rotating the grid by 90 degrees gives you essentially a different map with a different tactical arrangement. Rotating a grid by 90 degrees does not have this effect.
The problem here is trying to rotate a hex grid by 90 degrees. That is just a silly thing to try. A hex grid is invariant under rotations by 60 degrees though. Trying to rotate a square grid by 60 degrees also doesn't make much sense, does it?
 
I have always dreamed about a CIV game with hexagonal tiles! Amazing to see one's dream becoming true... :)
 
There doesn't have to be a perfect map made of hexagons, they could just make them go up to the tip of each poles and then have an unaccessible area. It would be kinda like Civ 4 but with more usable space so you could skirt around the poles and still cross over the top or bottom of the world. Or perhaps you could just jump across this "space" to a symmetrical tile on the opposing side but couldn't stop within this "space".

There could even be a bonus to be the first to discover a pole like the Civ 4 bonus to ship movement for circumventing the world. Naturally you would need certain techs to survive the extreme cold of the poles.

Anyways, point is that there are methods that could work if they play around with it a little without needing to resort to those pesky pentagons.

EDIT: You know... that still may not work. At least I'm out there on the edge! :p
 
May main arguement here is, and has always been, is about the the point of switching to hex grids from square grids.

Both have their issues, and neither solves all the problems any grid-based system will encounter on the very basis that it's a model so simplify the theoretical reality being represented. So why the switch? The ultimate answer is because it is different. Because it's new. However it is not neccesarily better. It seems like the decision to change was made first, and then the justification was made afterwards. None of the issues with square based grids is best solved by "let's use hexes instead", and many of the advantages of squares are sacrificed with this change.

Also, there are no 3d shapes that can be made simply of regular hexagons. It is not mathematically possible. The reason hexes tesselate is because the interior angles are 120 degrees, and you can combine three of them around athe 360 degrees of a signle point. The same goes with squares (4 times 90 degrees = 360 degrees) and equilateral triangles (6 times 60 degrees = 360 degrees). However in order to form a 3d shape from regular polygons, you need to have the sum of interior angles around any given point (when laid flat) to be less than 360 degrees, and you need at least three such polygons to form the corner. Squares and equilateral triangles work (3 time 90 degrees = 270 degrees, and 5 times 60 degrees = 300 degrees). Pentagons work, even though they do not tesselate (3 times 108 degrees = 324 degrees). Hexagons however do not work because 3 times 120 degrees is 360 degrees, resulting in a flat plane, not a 3d object. Likewise regular septagons, octagons, and so forth do not work because 3 times their interiro angles is greater than 360 degrees, which also explains why they do not tesselate either).

Maybe this is another bonus for square-based systems vs. hexes - you can make a 3d map if you do not mind it being a cube! Making square representations of curved features is something we've been doing for a long time, and a cube is basically just six squares. So each face would represent the view from that specific face, although you would get a low of skewed geography the further you travel away from the centre of each face. It'd certainly be a weird map... Something like this perhaps?
 
May main arguement here is, and has always been, is about the the point of switching to hex grids from square grids.

Both have their issues, and neither solves all the problems any grid-based system will encounter on the very basis that it's a model so simplify the theoretical reality being represented. So why the switch? The ultimate answer is because it is different. Because it's new. However it is not neccesarily better. It seems like the decision to change was made first, and then the justification was made afterwards. None of the issues with square based grids is best solved by "let's use hexes instead", and many of the advantages of squares are sacrificed with this change.

Or quite possibly the developers thought that the additional benefits provided by switching to hexagons outweighed any new problems. I know personally diagonals annoy the hell out of me.

Also, there are no 3d shapes that can be made simply of regular hexagons. It is not mathematically possible. The reason hexes tesselate is because the interior angles are 120 degrees, and you can combine three of them around athe 360 degrees of a signle point. The same goes with squares (4 times 90 degrees = 360 degrees) and equilateral triangles (6 times 60 degrees = 360 degrees). However in order to form a 3d shape from regular polygons, you need to have the sum of interior angles around any given point (when laid flat) to be less than 360 degrees, and you need at least three such polygons to form the corner. Squares and equilateral triangles work (3 time 90 degrees = 270 degrees, and 5 times 60 degrees = 300 degrees). Pentagons work, even though they do not tesselate (3 times 108 degrees = 324 degrees). Hexagons however do not work because 3 times 120 degrees is 360 degrees, resulting in a flat plane, not a 3d object. Likewise regular septagons, octagons, and so forth do not work because 3 times their interiro angles is greater than 360 degrees, which also explains why they do not tesselate either).

You don't need a perfect hexagonal sphere, just use slightly unregular hexagons and you can come up with a pretty good approximation of a sphere.

Maybe this is another bonus for square-based systems vs. hexes - you can make a 3d map if you do not mind it being a cube! Making square representations of curved features is something we've been doing for a long time, and a cube is basically just six squares. So each face would represent the view from that specific face, although you would get a low of skewed geography the further you travel away from the centre of each face. It'd certainly be a weird map... Something like this perhaps?

Yeah but its a cube. Maybe a cube can represent a globe better than a hexagonal-derived approximation, but
IT'S A CUBE.
 
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