I'm in the process of building a space themed game.

With that, comes the topic of landing on different planets, and then building and fighting there. So, I'm creating different small maps of planets.

I figured it would be nice to actually have the maps behave like the surface of an actual sphere.

That is, continuous movement around the map, no dead ends or corners. And the idea that no space has a positional advantage with regards to distance.

Simply saying that travel off of one edge of the map wraps you around to the other side doesn't accomplish that. That describes the topology of a torus, not a sphere. Notice that the poles are adjacent, not opposite.

While that might be an acceptable compromise for most purposes, I wanted to do better.

For one thing, you just can't accurately map the whole Earth this way.

Many playing boards have adapted this by allowing movement to the opposite side when traveling east or west, but not allowing wrapping north and south. (How silly it would be to move to the north pole and suddenly be in Antarctica?)

But there are some problems with this. Your options to get to the opposite side of the globe are reduced. No polar routes are possible. Furthermore, as spaces get closer to a pole, they become artificially too far apart.

Historically, this is mitigated by the fact that polar travel was largely infeasable. And so, these problems could safely be ignored in game design.

Once you move into hi-tech or sci-fi settings, the problem becomes increasingly relevant, as your units have the capability to travel the whole globe.

You can't model the polar regions concurrently with equatorial regions using such a system.

To solve this, I'm been mapping board spaces that try to reflect the realities of a sphere.

1) Distance from any particular space to the space on the opposite side of the planet is the same regardless of direction traveled.

2) Each space represents aproximatel equal area of coverage on the surface, even though some spaces will appear stretched in 2D.

3) All spaces should connect by edges, never by a single point. Squares laid out like a chessboard are problematic in this regard.

Below, is an image showing some solutions for different sized planets.

To show possible moves that wrap around the board, a lettered and colored dot appears on the edge of some spaces. The edge of such a space connects to the other edge with the corresponding dot.

In the image, the top row shows layouts for 1, 2, 4, and 6 space worlds. The 6 space world is analogous to a 6 sided die. Admittedly, the 2 and 4 space worlds are a bit awkward.

The middle row shows 2 different ways to map a world with 12 spaces. The black dots labeled A and B show two spaces that are opposite each other.

(These are similar to a d12, the first as if the die was standing on a point, the second as if the die was lying flat. Both choices have utility depending on how you want to depict the polar region.)

The last example is a globe with 32 spaces. Its topology is like the regions of a soccer ball.

Here, I've also illustrated how the distances remain constant.

Traveling from pole to pole is 5 spaces (Green arrow)

Travel from a space on near the equator to its opposite space is 5 spaces away. Equatorial route (Red arrow), and polar route (Blue arrow)

Furthermore, travel east and west when between the equator and poles (point A), describes a shorter path then when along the equator, and is also still 5 spaces away when going to its opposite space (point B).

All the above hold true even if wrapping off the map to the other side.

I also have a working map with 54 spaces. (Also, I have plans for even larger ones, but they are out of scope for my game)

For reference, I have superimposed a map of the Earth to sort of give an idea of how a game board migth be presented - though you'd likely have to tweak the positions of land masses a bit.

Unfortunately, I'm having a problem with getting a good map between 12 and 32 spaces. Something that has a distance to opposite at 4, currently a gap in my planet sizes.

I thought I had a one at 18 spaces, but it turned out that some points had shortest solutions of 3 instead of 4.

This seem to basically be a math problem, but I'm having trouble trying to look this stuff up. As such, my solutions have largely been the result of trial an error so far.

I guess my questions here are if anyone else has tried this, or something similar?

Are there any games that use such a system?

Does anyone have the necessary foundation in topology(?) to even be able to ask the right questions that I can search for a solution?

rellekmr wrote:Well, I addressed some of that in the original post.

The planet with 32 spaces is basicaly a soccer ball.

The 12 space, and 6 space planets are basicaly equivalent to 12 and 6 sided dies, respectively.

d20 does not work for a number of reasons. I think mainly because more than three spaces contribute to any given point.

Again, the problem comes from finding solutions for other numbers of spaces.

Unless there's a formula I can use, it's tricky to find solutions that have all spaces given equal position.

It doesn't work to simply sub-divide solutions I already have.

You'll notice that the spaces around the equator must be either = (2x number of rings vertical)

or you can use less if you can stager them such that an extra moves are needed.

Also, (building from the pole down) you can only increase the number of spaces in a ring by a multiple of the previous ring or you get problems of distance equity.

Finding the exceptions that work, is the dificult part. It's more of a fine art of balance at the moment.

On the bright side, I may have found a satisfactory solution for 26 spaces (with a half-way distance of 4)

It's not perfect, but I think it'll work.

The number of spaces in the rings, top to bottom, look like:

3

6

8

6

3

The tricky part is getting the ring of 6s to line up with the ring of 8.

Not all spaces will connect equally to the mid ring, and this can cause distance problems for some of the spaces.

But through delicate stagering and arrangement, I think I may have found an layout that balances out.

It should be noted that the cleaner arrangement of:

1

4

8

4

1

Does NOT work! All the spaces line up nice and easy, but it turns out that the spaces in the ring of 4 can hit any other space in 3 moves, whereas the other spaces all need 4 moves.

I might try 1,6,8,6,1 as a solution too, but my impression is that there's too much distance between 1 to 6 and too little between 6 to 8 to represent a convincing sphere.