# Go on a Sphere

Hi everyone,
Here is the Github Repo: GitHub - Holz231/Go-on-a-Sphere: Go on a Sphere

I have programmed Go in Python on a sphere. It’s bare bones, and you have to remove the captured stones yourself, but you can play Go on a sphere. It is only available in Python code and can only be played locally.
Would anyone be interested in trying it out and giving me some feedback?

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What does the board graph look like? Is your code on GitHub somewhere?

hey, i finished the code yesterday and at this Weekend i will create a githup repo.

the grid looks like the tangent adjusted grid you see here: Wraparound square tile maps on a sphere

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Ah, so it’s just topologically equivalent to how one might play on a cube?

I’ve actually played some cube go games

However, our graph was just slightly different. We didn’t have corner points with only three neighbors, but instead all points on our board has four neighbors.

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that sounds interisting, how would a cube have 4 neighbors at the corners? could you send me an example?
yes its basically a cube grid on a sphere

In my previous post, the preview box is a link to another forum thread where we discuss the concept, and how we implemented a few games, using both physical, paper prototypes and relaying moves via an OGS game.

Here is a picture from the first post of that thread that shows the basic idea of the board.

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I read through your link and saw that one, but at the corners you only got 3 connections, just like the grid on the sphere. Or did i miss something?

I think you missed that I said that we don’t have corner points.

We didn’t put any points directly on the physical corners or edges of the cube.

In yet another thread (which discusses the implementation of a Go server for playing Go variants), someone mentioned another way to have a sphere-like board that is quite distinct than just reshaping the cube:

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oh yeah i saw that one but there you got 5 connections, which changes alot of the capture dynamic i guess and the placement of the stones is quite irregular what makes it hard to see formations, i like the solution of squares on a sphere better, because almost every point has 4 connections, only the “corners” have 3 connections but thats kinda like in 2d where the board at the corners only has 2 connections.

these lines do not exist. But because its all painted on sharp cube it looks like if it exist

if we transform that cube into sphere like that:

then these lines would 100% disappear

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i see thanks for the explanation, so you just dont play on the edges and corners but i guess i see a problem with that, but please correct me if i am wrong, actually i would really want a solution with 4 normal points everywhere.

yes i get that, they are just an illusion occurring because of the folding of the cube, but look at the picture i send, my issue is different, i cant explain it to well with words, thats why i have drawn it. look at the connections the stone at the near of the right corner gets, isnt that weird to play like that?

yeah, its like that at corners of cube
but such sphere is easy to imagine, its possible to create real board like that
while attempt to make torus look like a sphere is something surreal

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so i guess the sphere solution is better? because you dont get those weird connections and just play on everythin even the “edges”, there are places with 3 lifes but as i said i think thats the best solution to it, and it kinda mimicks a 2d board in that sense

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I think that you are saying that you find it weird for there to be a 3-cycle around the corners of the cube?

Yes, the “Vorlon” cube version is no longer a bipartite graph, so odd-length cycles exist, whereas the other proposal is still a bipartite graph, and hence only has even-length cycles.

Having played the Vorlon variant twice (on cubes with 4x4 and 8x8 faces), I would say that the odd-cycle feature doesn’t really stand out as feeling quite different from normal Go. However, what does feel weird about Vorlon Cube Go is that it feels essentially like edge-less Go.

If the aim is to consider variants played on the surface of a cube, I think that these are just two different ways of doing it, and that it maybe comes down to subjective preference. The two graphs are duals of each other.

From a practical perspective, it might be a bit easier to manage physical prototypes of the Vorlon cube version (see photos in the other threads).

In the original aim of playing on a sphere, I feel that both approaches fall short, as they are more naturally interpreted as the surface of a cube, despite any spherical projection applied, since they lack the symmetry that I think should be suggested by a sphere.

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With the aim of considering other quartic graphs (i.e., each vertex has 4 neighbors) that approximate a spherical surface, here are some other options:

30 points: Icosidodecahedron - Wikipedia

60 points: Rhombicosidodecahedron - Wikipedia

120 points: Expanded icosidodecahedron - Wikipedia

Of course, these all have small 3-cycles (in the paths around the triangle faces), which could be viewed as weird.

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