change hexagons to octagons

[blind biker]

PawelS, if I understand your question correctly, the answer is no. A buckyball has precisely the same amount of sides regardless of the sphere it envelops, the size of tiles is a function of the radius of this sphere. So "scaling", i.e., adding more tiles of the same pattern will not produce the same shape. As a matter of fact, it will more than likely close at very ugly boundaries.

You can have any size buckyball-like shape, as long as you have 12 pentagons in them. And pentagons can be made from triangles just as hexagons.

 

[PieceOfMind]

Also, I don't know how you can say the 20-faced polyhedron made from equilateral triangles is any more spherical than the one made from only 4 triangles.

 

[El Caballerion]

Nope. I wont settled for anything less than icosahedrons.

 

[Jolly Rogerer]

I vote for phallus-shaped tiles!

The phallus shaped tile has been bandied about before, but it cannot actually be done, that's just a phallusy.

 

[Putmalk]

The phallus shaped tile has been bandied about before, but it cannot actually be done, that's just a phallusy.

Somebody made a funny.

 

[GenericPlayer]

Octagons is not far fetched. We had squares in Civ 4 and earlier, but since you could move through the corners (and not just the sides), they were de facto octagons. You had eight movement possibilities before, and now you just have 6.

 

[E66man]

Not true at all: you can have an infinite number of triangles forming a "sferical" (closed soccer ball) shape.

Note that I said 'regular' polygons. If you remove this restriction then yes, you are correct.

 

[blind biker]

Note that I said 'regular' polygons. If you remove this restriction then yes, you are correct.

You did say regular polygons, which equilateral triangles indisputably are.

 

[vulture2]

You did say regular polygons, which equilateral triangles indisputably are.

But you can't make anything spherical out of equilateral triangles. You can tile an icosohedron with them (with those 12 pesky pentagons), but if you want to 'inflate' the surface of the icosohedron to map it onto a sphere as closely as possible, you are no longer dealing with equilateral triangles. If you have enough of them, they won't be far from equilateral, but they won't, strictly, be so.

 

[blind biker]

But you can't make anything spherical out of equilateral triangles. You can tile an icosohedron with them (with those 12 pesky pentagons), but if you want to 'inflate' the surface of the icosohedron to map it onto a sphere as closely as possible, you are no longer dealing with equilateral triangles. If you have enough of them, they won't be far from equilateral, but they won't, strictly, be so.

You can make a "convex" pentagon with 5 equilateral triangles. (I am not sure if we're agreeing on this - please let me know.) And the hexagons are obviously made of 6 equilateral triangles. So your whole spheric structure is all composed of equilateral triangles.

 

[vulture2]

You can make a "convex" pentagon with 5 equilateral triangles. (I am not sure if we're agreeing on this - please let me know.)

agreed

And the hexagons are obviously made of 6 equilateral triangles. So your whole spheric structure is all composed of equilateral triangles.

But it's not spherical: it's a tiled icosohedron. ALl the equilateral triangles lie on one of the 20 planes of the icosohedron. To make all the vertices lie on the surface of a sphere, you have to shift them all outwards, and what you end up with isn't equiliateral triangles. It's nearly equilateral triangles. (Or regular pentagons with not-quite-regular hexagons (if you have more than 20 of them) if you want to group the triangles together into hexes).

 

[Zyxpsilon]

GC3 better not end up as "Elemental in Space"...although I love EWoM.

According to this & plenty more threads everywhere in Stardockia it might very well be.
GC3 deserves much more attention than this, as it is -- after all -- the main gaming product franchise of SD.
Nothing against Sins or Demi-God but Galactic gameplay Spockly_Fascinates me.

 

[Zyxpsilon]

Octagons is not far fetched. We had squares in Civ 4 and earlier, but since you could move through the corners (and not just the sides), they were de facto octagons. You had eight movement possibilities before, and now you just have 6.

That's why i was sooooo surprised when i realized they didn't use the whole 12 directions pattern.
Some may say it defeats the ZoC ruleset... but in certain cases - it could have been the only way to provide effective movement by gauntlets of units marching through battlefields.
Imagine a sneaky escape to such empty spots (barely a tile away) behind enemy lines!

 

[blind biker]

But it's not spherical: it's a tiled icosohedron. ALl the equilateral triangles lie on one of the 20 planes of the icosohedron. To make all the vertices lie on the surface of a sphere, you have to shift them all outwards, and what you end up with isn't equiliateral triangles. It's nearly equilateral triangles. (Or regular pentagons with not-quite-regular hexagons (if you have more than 20 of them) if you want to group the triangles together into hexes).

OK, you are 100% correct.

What can I say: to make the world look spherical, those triangles will have to be bent a little (non-euclidian geometry?) and yes, the triangles in the 12 pentagons will have to be a bit non-equilateral. But all in all, I think it would still look great. I think.

 

[PawelS]

Thanks for clarification. Maybe Civ6 will have "icosohedronal maps" But there may be problems with the 12 pentagon tiles, for example a city founded there will have less tiles to use from the start.

 

[factorof2]

Sort of blind biker, it would have the intrinsic geometry of the sphere, that is your principal curvatures all have the same sign for any point on your surface and your triangles will exhibit some "strange" properties, in that they can have angle sums greater than 180 degrees and the like.

 

[carlisimo]

You guys aren’t seriously asking for triangles, are you? Being limited to three directions of movement would drive me crazy… and if you allow corner movement then you might as well just keep the hexagons.

 

[blind biker]

You guys aren’t seriously asking for triangles, are you? Being limited to three directions of movement would drive me crazy… and if you allow corner movement then you might as well just keep the hexagons.

Wait a second: let me be perfectly clear with you: there is nothing wrong with hexes, apart from one thing, and that they don't allow for spherical worlds/maps. Triangles, on the other hand, with corner movement, would allow for spherical worlds. That's all we're saying... aren't we?


And I humbly submit to you that a spherical world for Civilization would look and feel f*cking awesome. Just my humble opinion.

 

[carlisimo]

I'm not taking a stand on spherical vs. flat; all I’m saying is I don’t want to be limited to three directions of movement per tile. On the other hand, corner movement with triangles could allow twelve directions and that seems excessive.

 

[blind biker]

On the other hand, corner movement with triangles could allow twelve directions and that seems excessive.

You can't have too much of a good thing, as my granma would say while she'd drink a second cup of LSD-laced tea. She was a wise woman, so heed her advice.